gf(2) Iterate until all irreducible factors of f0 are found

f0 = b0000000000000000000000000000000000000000000000000000000001100111
f0 = 0x0000000000000067
f0 = x6 + x5 + x2 + x + 1

Find at least one irreducible factor of f0, if it exists.

f0 is irreducible.

Irreducible factors:

f0 = (b1100111)
f0 = (0x67)
f0 = (x6 + x5 + x2 + x + 1)