gf(2) Calculating the gcd (greatest common divisor)
Euclid's Algorithm
c = gcd(a0,b0)
a0 = b01100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001
a0 = 0x65ee6bda0b324559661859ebf3268b49
a0 = x126 + x125 + x122 + x120 + x119 + x118 + x117 + x115 + x114 + x113 + x110 + x109 + x107 + x105 + x104 + x103 + x102 + x100 + x99 + x97 + x91 + x89 + x88 + x85 + x84 + x81 + x78 + x74 + x72 + x70 + x68 + x67 + x64 + x62 + x61 + x58 + x57 + x52 + x51 + x46 + x44 + x43 + x40 + x39 + x38 + x37 + x35 + x33 + x32 + x31 + x30 + x29 + x28 + x25 + x24 + x21 + x18 + x17 + x15 + x11 + x9 + x8 + x6 + x3 + 1
b0 = b00010000010101010001010101000101000001010001000100000000000001000001000100000100000001000101010101010001000100010100010100000100
b0 = 0x10551545051100041104045551114504
b0 = x124 + x118 + x116 + x114 + x112 + x108 + x106 + x104 + x102 + x98 + x96 + x90 + x88 + x84 + x80 + x66 + x60 + x56 + x50 + x42 + x38 + x36 + x34 + x32 + x30 + x28 + x24 + x20 + x16 + x14 + x10 + x8 + x2
Find r0 = a0 % b0
r0 = b00000100000100000001010001000100000101010101010001000101010000010000000000000000010000000001010000010101010000010001010101010001
r0 = 0x04101444155445410000401415411551
r0 = x122 + x116 + x108 + x106 + x102 + x98 + x92 + x90 + x88 + x86 + x84 + x82 + x78 + x74 + x72 + x70 + x64 + x46 + x36 + x34 + x28 + x26 + x24 + x22 + x16 + x12 + x10 + x8 + x6 + x4 + 1
r0 is not zero nor one, so continue...
a1 = b0
a1 = b00010000010101010001010101000101000001010001000100000000000001000001000100000100000001000101010101010001000100010100010100000100
a1 = 0x10551545051100041104045551114504
a1 = x124 + x118 + x116 + x114 + x112 + x108 + x106 + x104 + x102 + x98 + x96 + x90 + x88 + x84 + x80 + x66 + x60 + x56 + x50 + x42 + x38 + x36 + x34 + x32 + x30 + x28 + x24 + x20 + x16 + x14 + x10 + x8 + x2
b1 = r0
b1 = b00000100000100000001010001000100000101010101010001000101010000010000000000000000010000000001010000010101010000010001010101010001
b1 = 0x04101444155445410000401415411551
b1 = x122 + x116 + x108 + x106 + x102 + x98 + x92 + x90 + x88 + x86 + x84 + x82 + x78 + x74 + x72 + x70 + x64 + x46 + x36 + x34 + x28 + x26 + x24 + x22 + x16 + x12 + x10 + x8 + x6 + x4 + 1
Find r1 = a1 % b1
r1 = b00000000000101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000
r1 = 0x00154455504015001105040504151040
r1 = x116 + x114 + x112 + x110 + x106 + x102 + x100 + x98 + x96 + x94 + x92 + x86 + x76 + x74 + x72 + x60 + x56 + x50 + x48 + x42 + x34 + x32 + x26 + x20 + x18 + x16 + x12 + x6
r1 is not zero nor one, so continue...
a2 = b1
a2 = b00000100000100000001010001000100000101010101010001000101010000010000000000000000010000000001010000010101010000010001010101010001
a2 = 0x04101444155445410000401415411551
a2 = x122 + x116 + x108 + x106 + x102 + x98 + x92 + x90 + x88 + x86 + x84 + x82 + x78 + x74 + x72 + x70 + x64 + x46 + x36 + x34 + x28 + x26 + x24 + x22 + x16 + x12 + x10 + x8 + x6 + x4 + 1
b2 = r1
b2 = b00000000000101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000
b2 = 0x00154455504015001105040504151040
b2 = x116 + x114 + x112 + x110 + x106 + x102 + x100 + x98 + x96 + x94 + x92 + x86 + x76 + x74 + x72 + x60 + x56 + x50 + x48 + x42 + x34 + x32 + x26 + x20 + x18 + x16 + x12 + x6
Find r2 = a2 % b2
r2 = b00000000000000000000000000010000010100010001000001000000010001000100000000010100000001010000000001010101010000010001000100010001
r2 = 0x00000010511040444014050055411111
r2 = x100 + x94 + x92 + x88 + x84 + x78 + x70 + x66 + x62 + x52 + x50 + x42 + x40 + x30 + x28 + x26 + x24 + x22 + x16 + x12 + x8 + x4 + 1
r2 is not zero nor one, so continue...
a3 = b2
a3 = b00000000000101010100010001010101010100000100000000010101000000000001000100000101000001000000010100000100000101010001000001000000
a3 = 0x00154455504015001105040504151040
a3 = x116 + x114 + x112 + x110 + x106 + x102 + x100 + x98 + x96 + x94 + x92 + x86 + x76 + x74 + x72 + x60 + x56 + x50 + x48 + x42 + x34 + x32 + x26 + x20 + x18 + x16 + x12 + x6
b3 = r2
b3 = b00000000000000000000000000010000010100010001000001000000010001000100000000010100000001010000000001010101010000010001000100010001
b3 = 0x00000010511040444014050055411111
b3 = x100 + x94 + x92 + x88 + x84 + x78 + x70 + x66 + x62 + x52 + x50 + x42 + x40 + x30 + x28 + x26 + x24 + x22 + x16 + x12 + x8 + x4 + 1
Find r3 = a3 % b3
r3 = b00000000000000000000000000000100010000000000000100010000000000000101000000010100000000010101010100010000000101010000010000000000
r3 = 0x00000004400110005014015510150400
r3 = x98 + x94 + x80 + x76 + x62 + x60 + x52 + x50 + x40 + x38 + x36 + x34 + x32 + x28 + x20 + x18 + x16 + x10
r3 is not zero nor one, so continue...
a4 = b3
a4 = b00000000000000000000000000010000010100010001000001000000010001000100000000010100000001010000000001010101010000010001000100010001
a4 = 0x00000010511040444014050055411111
a4 = x100 + x94 + x92 + x88 + x84 + x78 + x70 + x66 + x62 + x52 + x50 + x42 + x40 + x30 + x28 + x26 + x24 + x22 + x16 + x12 + x8 + x4 + 1
b4 = r3
b4 = b00000000000000000000000000000100010000000000000100010000000000000101000000010100000000010101010100010000000101010000010000000000
b4 = 0x00000004400110005014015510150400
b4 = x98 + x94 + x80 + x76 + x62 + x60 + x52 + x50 + x40 + x38 + x36 + x34 + x32 + x28 + x20 + x18 + x16 + x10
Find r4 = a4 % b4
r4 = b00000000000000000000000000000001010100010001010000000000010001010000000001000100000000000101010000010101000101010000000100010001
r4 = 0x00000001511400450044005415150111
r4 = x96 + x94 + x92 + x88 + x84 + x82 + x70 + x66 + x64 + x54 + x50 + x38 + x36 + x34 + x28 + x26 + x24 + x20 + x18 + x16 + x8 + x4 + 1
r4 is not zero nor one, so continue...
a5 = b4
a5 = b00000000000000000000000000000100010000000000000100010000000000000101000000010100000000010101010100010000000101010000010000000000
a5 = 0x00000004400110005014015510150400
a5 = x98 + x94 + x80 + x76 + x62 + x60 + x52 + x50 + x40 + x38 + x36 + x34 + x32 + x28 + x20 + x18 + x16 + x10
b5 = r4
b5 = b00000000000000000000000000000001010100010001010000000000010001010000000001000100000000000101010000010101000101010000000100010001
b5 = 0x00000001511400450044005415150111
b5 = x96 + x94 + x92 + x88 + x84 + x82 + x70 + x66 + x64 + x54 + x50 + x38 + x36 + x34 + x28 + x26 + x24 + x20 + x18 + x16 + x8 + x4 + 1
Find r5 = a5 % b5
r5 = b00000000000000000000000000000000010101010100010100010001010100010101000101000000000000000101000101010001010101000000000101010101
r5 = 0x00000000554511515140005151540155
r5 = x94 + x92 + x90 + x88 + x86 + x82 + x80 + x76 + x72 + x70 + x68 + x64 + x62 + x60 + x56 + x54 + x38 + x36 + x32 + x30 + x28 + x24 + x22 + x20 + x18 + x8 + x6 + x4 + x2 + 1
r5 is not zero nor one, so continue...
a6 = b5
a6 = b00000000000000000000000000000001010100010001010000000000010001010000000001000100000000000101010000010101000101010000000100010001
a6 = 0x00000001511400450044005415150111
a6 = x96 + x94 + x92 + x88 + x84 + x82 + x70 + x66 + x64 + x54 + x50 + x38 + x36 + x34 + x28 + x26 + x24 + x20 + x18 + x16 + x8 + x4 + 1
b6 = r5
b6 = b00000000000000000000000000000000010101010100010100010001010100010101000101000000000000000101000101010001010101000000000101010101
b6 = 0x00000000554511515140005151540155
b6 = x94 + x92 + x90 + x88 + x86 + x82 + x80 + x76 + x72 + x70 + x68 + x64 + x62 + x60 + x56 + x54 + x38 + x36 + x32 + x30 + x28 + x24 + x22 + x20 + x18 + x8 + x6 + x4 + x2 + 1
Find r6 = a6 % b6
r6 = b00000000000000000000000000000000000001000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101
r6 = 0x00000000040045004544011150450445
r6 = x90 + x78 + x74 + x72 + x62 + x58 + x56 + x54 + x50 + x40 + x36 + x32 + x30 + x28 + x22 + x18 + x16 + x10 + x6 + x2 + 1
r6 is not zero nor one, so continue...
a7 = b6
a7 = b00000000000000000000000000000000010101010100010100010001010100010101000101000000000000000101000101010001010101000000000101010101
a7 = 0x00000000554511515140005151540155
a7 = x94 + x92 + x90 + x88 + x86 + x82 + x80 + x76 + x72 + x70 + x68 + x64 + x62 + x60 + x56 + x54 + x38 + x36 + x32 + x30 + x28 + x24 + x22 + x20 + x18 + x8 + x6 + x4 + x2 + 1
b7 = r6
b7 = b00000000000000000000000000000000000001000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101
b7 = 0x00000000040045004544011150450445
b7 = x90 + x78 + x74 + x72 + x62 + x58 + x56 + x54 + x50 + x40 + x36 + x32 + x30 + x28 + x22 + x18 + x16 + x10 + x6 + x2 + 1
Find r7 = a7 % b7
r7 = b00000000000000000000000000000000000000010100000000010000010101000101010101010100000101000001000001000100010101010101000001010100
r7 = 0x00000000014010545554141044555054
r7 = x88 + x86 + x76 + x70 + x68 + x66 + x62 + x60 + x58 + x56 + x54 + x52 + x50 + x44 + x42 + x36 + x30 + x26 + x22 + x20 + x18 + x16 + x14 + x12 + x6 + x4 + x2
r7 is not zero nor one, so continue...
a8 = b7
a8 = b00000000000000000000000000000000000001000000000001000101000000000100010101000100000000010001000101010000010001010000010001000101
a8 = 0x00000000040045004544011150450445
a8 = x90 + x78 + x74 + x72 + x62 + x58 + x56 + x54 + x50 + x40 + x36 + x32 + x30 + x28 + x22 + x18 + x16 + x10 + x6 + x2 + 1
b8 = r7
b8 = b00000000000000000000000000000000000000010100000000010000010101000101010101010100000101000001000001000100010101010101000001010100
b8 = 0x00000000014010545554141044555054
b8 = x88 + x86 + x76 + x70 + x68 + x66 + x62 + x60 + x58 + x56 + x54 + x52 + x50 + x44 + x42 + x36 + x30 + x26 + x22 + x20 + x18 + x16 + x14 + x12 + x6 + x4 + x2
Find r8 = a8 % b8
r8 = b00000000000000000000000000000000000000000100000000010100000001010100010101000000010001010100000000000101010001010001010101000001
r8 = 0x00000000004014054540454005451541
r8 = x86 + x76 + x74 + x66 + x64 + x62 + x58 + x56 + x54 + x46 + x42 + x40 + x38 + x26 + x24 + x22 + x18 + x16 + x12 + x10 + x8 + x6 + 1
r8 is not zero nor one, so continue...
a9 = b8
a9 = b00000000000000000000000000000000000000010100000000010000010101000101010101010100000101000001000001000100010101010101000001010100
a9 = 0x00000000014010545554141044555054
a9 = x88 + x86 + x76 + x70 + x68 + x66 + x62 + x60 + x58 + x56 + x54 + x52 + x50 + x44 + x42 + x36 + x30 + x26 + x22 + x20 + x18 + x16 + x14 + x12 + x6 + x4 + x2
b9 = r8
b9 = b00000000000000000000000000000000000000000100000000010100000001010100010101000000010001010100000000000101010001010001010101000001
b9 = 0x00000000004014054540454005451541
b9 = x86 + x76 + x74 + x66 + x64 + x62 + x58 + x56 + x54 + x46 + x42 + x40 + x38 + x26 + x24 + x22 + x18 + x16 + x12 + x10 + x8 + x6 + 1
Find r9 = a9 % b9
r9 = b00000000000000000000000000000000000000000000000001010100010001000000010100010101010001000101000001010100000001000001000000010001
r9 = 0x00000000000054440515445054041011
r9 = x78 + x76 + x74 + x70 + x66 + x58 + x56 + x52 + x50 + x48 + x46 + x42 + x38 + x36 + x30 + x28 + x26 + x18 + x12 + x4 + 1
r9 is not zero nor one, so continue...
a10 = b9
a10 = b00000000000000000000000000000000000000000100000000010100000001010100010101000000010001010100000000000101010001010001010101000001
a10 = 0x00000000004014054540454005451541
a10 = x86 + x76 + x74 + x66 + x64 + x62 + x58 + x56 + x54 + x46 + x42 + x40 + x38 + x26 + x24 + x22 + x18 + x16 + x12 + x10 + x8 + x6 + 1
b10 = r9
b10 = b00000000000000000000000000000000000000000000000001010100010001000000010100010101010001000101000001010100000001000001000000010001
b10 = 0x00000000000054440515445054041011
b10 = x78 + x76 + x74 + x70 + x66 + x58 + x56 + x52 + x50 + x48 + x46 + x42 + x38 + x36 + x30 + x28 + x26 + x18 + x12 + x4 + 1
Find r10 = a10 % b10
r10 = b00000000000000000000000000000000000000000000000000010000000100010000000100000000000100000100000001010000010000010100000001000101
r10 = 0x00000000000010110100104050414045
r10 = x76 + x68 + x64 + x56 + x44 + x38 + x30 + x28 + x22 + x16 + x14 + x6 + x2 + 1
r10 is not zero nor one, so continue...
a11 = b10
a11 = b00000000000000000000000000000000000000000000000001010100010001000000010100010101010001000101000001010100000001000001000000010001
a11 = 0x00000000000054440515445054041011
a11 = x78 + x76 + x74 + x70 + x66 + x58 + x56 + x52 + x50 + x48 + x46 + x42 + x38 + x36 + x30 + x28 + x26 + x18 + x12 + x4 + 1
b11 = r10
b11 = b00000000000000000000000000000000000000000000000000010000000100010000000100000000000100000100000001010000010000010100000001000101
b11 = 0x00000000000010110100104050414045
b11 = x76 + x68 + x64 + x56 + x44 + x38 + x30 + x28 + x22 + x16 + x14 + x6 + x2 + 1
Find r11 = a11 % b11
r11 = b00000000000000000000000000000000000000000000000000000100000100010000000000010101000101010001000101000101010000000101000101000000
r11 = 0x00000000000004110015151145405140
r11 = x74 + x68 + x64 + x52 + x50 + x48 + x44 + x42 + x40 + x36 + x32 + x30 + x26 + x24 + x22 + x14 + x12 + x8 + x6
r11 is not zero nor one, so continue...
a12 = b11
a12 = b00000000000000000000000000000000000000000000000000010000000100010000000100000000000100000100000001010000010000010100000001000101
a12 = 0x00000000000010110100104050414045
a12 = x76 + x68 + x64 + x56 + x44 + x38 + x30 + x28 + x22 + x16 + x14 + x6 + x2 + 1
b12 = r11
b12 = b00000000000000000000000000000000000000000000000000000100000100010000000000010101000101010001000101000101010000000101000101000000
b12 = 0x00000000000004110015151145405140
b12 = x74 + x68 + x64 + x52 + x50 + x48 + x44 + x42 + x40 + x36 + x32 + x30 + x26 + x24 + x22 + x14 + x12 + x8 + x6
Find r12 = a12 % b12
r12 = b00000000000000000000000000000000000000000000000000000000010101010000000101010100010001000000010101000101010000000000010101000101
r12 = 0x00000000000000550154440545400545
r12 = x70 + x68 + x66 + x64 + x56 + x54 + x52 + x50 + x46 + x42 + x34 + x32 + x30 + x26 + x24 + x22 + x10 + x8 + x6 + x2 + 1
r12 is not zero nor one, so continue...
a13 = b12
a13 = b00000000000000000000000000000000000000000000000000000100000100010000000000010101000101010001000101000101010000000101000101000000
a13 = 0x00000000000004110015151145405140
a13 = x74 + x68 + x64 + x52 + x50 + x48 + x44 + x42 + x40 + x36 + x32 + x30 + x26 + x24 + x22 + x14 + x12 + x8 + x6
b13 = r12
b13 = b00000000000000000000000000000000000000000000000000000000010101010000000101010100010001000000010101000101010000000000010101000101
b13 = 0x00000000000000550154440545400545
b13 = x70 + x68 + x66 + x64 + x56 + x54 + x52 + x50 + x46 + x42 + x34 + x32 + x30 + x26 + x24 + x22 + x10 + x8 + x6 + x2 + 1
Find r13 = a13 % b13
r13 = b00000000000000000000000000000000000000000000000000000000000101010001000000000000010001010101000000000100010000000001000000000100
r13 = 0x00000000000000151000455004401004
r13 = x68 + x66 + x64 + x60 + x46 + x42 + x40 + x38 + x36 + x26 + x22 + x12 + x2
r13 is not zero nor one, so continue...
a14 = b13
a14 = b00000000000000000000000000000000000000000000000000000000010101010000000101010100010001000000010101000101010000000000010101000101
a14 = 0x00000000000000550154440545400545
a14 = x70 + x68 + x66 + x64 + x56 + x54 + x52 + x50 + x46 + x42 + x34 + x32 + x30 + x26 + x24 + x22 + x10 + x8 + x6 + x2 + 1
b14 = r13
b14 = b00000000000000000000000000000000000000000000000000000000000101010001000000000000010001010101000000000100010000000001000000000100
b14 = 0x00000000000000151000455004401004
b14 = x68 + x66 + x64 + x60 + x46 + x42 + x40 + x38 + x36 + x26 + x22 + x12 + x2
Find r14 = a14 % b14
r14 = b00000000000000000000000000000000000000000000000000000000000000010100000101010101010100010100010101010100010000000100010101010101
r14 = 0x00000000000000014155514554404555
r14 = x64 + x62 + x56 + x54 + x52 + x50 + x48 + x46 + x44 + x40 + x38 + x34 + x32 + x30 + x28 + x26 + x22 + x14 + x10 + x8 + x6 + x4 + x2 + 1
r14 is not zero nor one, so continue...
a15 = b14
a15 = b00000000000000000000000000000000000000000000000000000000000101010001000000000000010001010101000000000100010000000001000000000100
a15 = 0x00000000000000151000455004401004
a15 = x68 + x66 + x64 + x60 + x46 + x42 + x40 + x38 + x36 + x26 + x22 + x12 + x2
b15 = r14
b15 = b00000000000000000000000000000000000000000000000000000000000000010100000101010101010100010100010101010100010000000100010101010101
b15 = 0x00000000000000014155514554404555
b15 = x64 + x62 + x56 + x54 + x52 + x50 + x48 + x46 + x44 + x40 + x38 + x34 + x32 + x30 + x28 + x26 + x22 + x14 + x10 + x8 + x6 + x4 + x2 + 1
Find r15 = a15 % b15
r15 = b00000000000000000000000000000000000000000000000000000000000000000100010000000000000000000100000000010100000001000000000000000001
r15 = 0x00000000000000004400004014040001
r15 = x62 + x58 + x38 + x28 + x26 + x18 + 1
r15 is not zero nor one, so continue...
a16 = b15
a16 = b00000000000000000000000000000000000000000000000000000000000000010100000101010101010100010100010101010100010000000100010101010101
a16 = 0x00000000000000014155514554404555
a16 = x64 + x62 + x56 + x54 + x52 + x50 + x48 + x46 + x44 + x40 + x38 + x34 + x32 + x30 + x28 + x26 + x22 + x14 + x10 + x8 + x6 + x4 + x2 + 1
b16 = r15
b16 = b00000000000000000000000000000000000000000000000000000000000000000100010000000000000000000100000000010100000001000000000000000001
b16 = 0x00000000000000004400004014040001
b16 = x62 + x58 + x38 + x28 + x26 + x18 + 1
Find r16 = a16 % b16
r16 = b00000000000000000000000000000000000000000000000000000000000000000001010101010101010100000000010100010000010101000100010101010000
r16 = 0x00000000000000001555500510544550
r16 = x60 + x58 + x56 + x54 + x52 + x50 + x48 + x46 + x44 + x34 + x32 + x28 + x22 + x20 + x18 + x14 + x10 + x8 + x6 + x4
r16 is not zero nor one, so continue...
a17 = b16
a17 = b00000000000000000000000000000000000000000000000000000000000000000100010000000000000000000100000000010100000001000000000000000001
a17 = 0x00000000000000004400004014040001
a17 = x62 + x58 + x38 + x28 + x26 + x18 + 1
b17 = r16
b17 = b00000000000000000000000000000000000000000000000000000000000000000001010101010101010100000000010100010000010101000100010101010000
b17 = 0x00000000000000001555500510544550
b17 = x60 + x58 + x56 + x54 + x52 + x50 + x48 + x46 + x44 + x34 + x32 + x28 + x22 + x20 + x18 + x14 + x10 + x8 + x6 + x4
Find r17 = a17 % b17
r17 = b00000000000000000000000000000000000000000000000000000000000000000000010000000000000100000101000101000101000000010101000000010001
r17 = 0x00000000000000000400105145015011
r17 = x58 + x44 + x38 + x36 + x32 + x30 + x26 + x24 + x16 + x14 + x12 + x4 + 1
r17 is not zero nor one, so continue...
a18 = b17
a18 = b00000000000000000000000000000000000000000000000000000000000000000001010101010101010100000000010100010000010101000100010101010000
a18 = 0x00000000000000001555500510544550
a18 = x60 + x58 + x56 + x54 + x52 + x50 + x48 + x46 + x44 + x34 + x32 + x28 + x22 + x20 + x18 + x14 + x10 + x8 + x6 + x4
b18 = r17
b18 = b00000000000000000000000000000000000000000000000000000000000000000000010000000000000100000101000101000101000000010101000000010001
b18 = 0x00000000000000000400105145015011
b18 = x58 + x44 + x38 + x36 + x32 + x30 + x26 + x24 + x16 + x14 + x12 + x4 + 1
Find r18 = a18 % b18
r18 = b00000000000000000000000000000000000000000000000000000000000000000000000101010101000000010001000101000001010100000101010100000101
r18 = 0x00000000000000000155011141505505
r18 = x56 + x54 + x52 + x50 + x48 + x40 + x36 + x32 + x30 + x24 + x22 + x20 + x14 + x12 + x10 + x8 + x2 + 1
r18 is not zero nor one, so continue...
a19 = b18
a19 = b00000000000000000000000000000000000000000000000000000000000000000000010000000000000100000101000101000101000000010101000000010001
a19 = 0x00000000000000000400105145015011
a19 = x58 + x44 + x38 + x36 + x32 + x30 + x26 + x24 + x16 + x14 + x12 + x4 + 1
b19 = r18
b19 = b00000000000000000000000000000000000000000000000000000000000000000000000101010101000000010001000101000001010100000101010100000101
b19 = 0x00000000000000000155011141505505
b19 = x56 + x54 + x52 + x50 + x48 + x40 + x36 + x32 + x30 + x24 + x22 + x20 + x14 + x12 + x10 + x8 + x2 + 1
Find r19 = a19 % b19
r19 = b00000000000000000000000000000000000000000000000000000000000000000000000000000001000101010000010100000001000100000101000100000000
r19 = 0x00000000000000000001150501105100
r19 = x48 + x44 + x42 + x40 + x34 + x32 + x24 + x20 + x14 + x12 + x8
r19 is not zero nor one, so continue...
a20 = b19
a20 = b00000000000000000000000000000000000000000000000000000000000000000000000101010101000000010001000101000001010100000101010100000101
a20 = 0x00000000000000000155011141505505
a20 = x56 + x54 + x52 + x50 + x48 + x40 + x36 + x32 + x30 + x24 + x22 + x20 + x14 + x12 + x10 + x8 + x2 + 1
b20 = r19
b20 = b00000000000000000000000000000000000000000000000000000000000000000000000000000001000101010000010100000001000100000101000100000000
b20 = 0x00000000000000000001150501105100
b20 = x48 + x44 + x42 + x40 + x34 + x32 + x24 + x20 + x14 + x12 + x8
Find r20 = a20 % b20
r20 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000001000100000100010000010001000000000000000101
r20 = 0x00000000000000000000044110440005
r20 = x42 + x38 + x32 + x28 + x22 + x18 + x2 + 1
r20 is not zero nor one, so continue...
a21 = b20
a21 = b00000000000000000000000000000000000000000000000000000000000000000000000000000001000101010000010100000001000100000101000100000000
a21 = 0x00000000000000000001150501105100
a21 = x48 + x44 + x42 + x40 + x34 + x32 + x24 + x20 + x14 + x12 + x8
b21 = r20
b21 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000001000100000100010000010001000000000000000101
b21 = 0x00000000000000000000044110440005
b21 = x42 + x38 + x32 + x28 + x22 + x18 + x2 + 1
Find r21 = a21 % b21
r21 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000010101000101000001000101
r21 = 0x00000000000000000000010000545045
r21 = x40 + x22 + x20 + x18 + x14 + x12 + x6 + x2 + 1
r21 is not zero nor one, so continue...
a22 = b21
a22 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000001000100000100010000010001000000000000000101
a22 = 0x00000000000000000000044110440005
a22 = x42 + x38 + x32 + x28 + x22 + x18 + x2 + 1
b22 = r21
b22 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000010101000101000001000101
b22 = 0x00000000000000000000010000545045
b22 = x40 + x22 + x20 + x18 + x14 + x12 + x6 + x2 + 1
Find r22 = a22 % b22
r22 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000100010001000101010100000100010001
r22 = 0x00000000000000000000004111154111
r22 = x38 + x32 + x28 + x24 + x20 + x18 + x16 + x14 + x8 + x4 + 1
r22 is not zero nor one, so continue...
a23 = b22
a23 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000000000000010101000101000001000101
a23 = 0x00000000000000000000010000545045
a23 = x40 + x22 + x20 + x18 + x14 + x12 + x6 + x2 + 1
b23 = r22
b23 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000100010001000101010100000100010001
b23 = 0x00000000000000000000004111154111
b23 = x38 + x32 + x28 + x24 + x20 + x18 + x16 + x14 + x8 + x4 + 1
Find r23 = a23 % b23
r23 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000100000000010101010000000001
r23 = 0x00000000000000000000000444015401
r23 = x34 + x30 + x26 + x16 + x14 + x12 + x10 + 1
r23 is not zero nor one, so continue...
a24 = b23
a24 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100000100010001000101010100000100010001
a24 = 0x00000000000000000000004111154111
a24 = x38 + x32 + x28 + x24 + x20 + x18 + x16 + x14 + x8 + x4 + 1
b24 = r23
b24 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000100000000010101010000000001
b24 = 0x00000000000000000000000444015401
b24 = x34 + x30 + x26 + x16 + x14 + x12 + x10 + 1
Find r24 = a24 % b24
r24 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010101000000010101010100000000
r24 = 0x00000000000000000000000115015500
r24 = x32 + x28 + x26 + x24 + x16 + x14 + x12 + x10 + x8
r24 is not zero nor one, so continue...
a25 = b24
a25 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000100000000010101010000000001
a25 = 0x00000000000000000000000444015401
a25 = x34 + x30 + x26 + x16 + x14 + x12 + x10 + 1
b25 = r24
b25 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010101000000010101010100000000
b25 = 0x00000000000000000000000115015500
b25 = x32 + x28 + x26 + x24 + x16 + x14 + x12 + x10 + x8
Find r25 = a25 % b25
r25 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000001000000000000000001
r25 = 0x00000000000000000000000010040001
r25 = x28 + x18 + 1
r25 is not zero nor one, so continue...
a26 = b25
a26 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000100010101000000010101010100000000
a26 = 0x00000000000000000000000115015500
a26 = x32 + x28 + x26 + x24 + x16 + x14 + x12 + x10 + x8
b26 = r25
b26 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000001000000000000000001
b26 = 0x00000000000000000000000010040001
b26 = x28 + x18 + 1
Find r26 = a26 % b26
r26 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101010001010101010100010001
r26 = 0x00000000000000000000000005455511
r26 = x26 + x24 + x22 + x18 + x16 + x14 + x12 + x10 + x8 + x4 + 1
r26 is not zero nor one, so continue...
a27 = b26
a27 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010000000001000000000000000001
a27 = 0x00000000000000000000000010040001
a27 = x28 + x18 + 1
b27 = r26
b27 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101010001010101010100010001
b27 = 0x00000000000000000000000005455511
b27 = x26 + x24 + x22 + x18 + x16 + x14 + x12 + x10 + x8 + x4 + 1
Find r27 = a27 % b27
r27 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010101000000000101010100
r27 = 0x00000000000000000000000000540154
r27 = x22 + x20 + x18 + x8 + x6 + x4 + x2
r27 is not zero nor one, so continue...
a28 = b27
a28 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101010001010101010100010001
a28 = 0x00000000000000000000000005455511
a28 = x26 + x24 + x22 + x18 + x16 + x14 + x12 + x10 + x8 + x4 + 1
b28 = r27
b28 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010101000000000101010100
b28 = 0x00000000000000000000000000540154
b28 = x22 + x20 + x18 + x8 + x6 + x4 + x2
Find r28 = a28 % b28
r28 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001010100000001010001
r28 = 0x00000000000000000000000000054051
r28 = x18 + x16 + x14 + x6 + x4 + 1
r28 is not zero nor one, so continue...
a29 = b28
a29 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010101000000000101010100
a29 = 0x00000000000000000000000000540154
a29 = x22 + x20 + x18 + x8 + x6 + x4 + x2
b29 = r28
b29 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001010100000001010001
b29 = 0x00000000000000000000000000054051
b29 = x18 + x16 + x14 + x6 + x4 + 1
Find r29 = a29 % b29
r29 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000100
r29 = 0x00000000000000000000000000000444
r29 = x10 + x6 + x2
r29 is not zero nor one, so continue...
a30 = b29
a30 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001010100000001010001
a30 = 0x00000000000000000000000000054051
a30 = x18 + x16 + x14 + x6 + x4 + 1
b30 = r29
b30 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000100
b30 = 0x00000000000000000000000000000444
b30 = x10 + x6 + x2
Find r30 = a30 % b30
r30 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101
r30 = 0x00000000000000000000000000000005
r30 = x2 + 1
r30 is not zero nor one, so continue...
a31 = b30
a31 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010001000100
a31 = 0x00000000000000000000000000000444
a31 = x10 + x6 + x2
b31 = r30
b31 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000101
b31 = 0x00000000000000000000000000000005
b31 = x2 + 1
Find r31 = a31 % b31
r31 = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
r31 = 0x00000000000000000000000000000001
r31 = 1
r31 is one, so gcd(a,b) is one (i.e. coprime/relatively prime)
See also: