The greatest common factor of [tex] x^{6} [/tex] and [tex] x^{4} [/tex] is [tex] x^{4} [/tex]. We can get this answer by knowing that a GCF is the greatest number that divides a and b evenly (without a remainder). In this case, the answer is [tex] x^{4} [/tex] because by multiply [tex] x^{4} [/tex] by [tex] x^{2} [/tex], we get [tex] x^{6} [/tex], showing that it's divisible. We know that no number greater than [tex] x^{4} [/tex] is a GCF because [tex] x^{4} [/tex] is equal to one of the numbers, so multiplying by anything larger than [tex] x^{4} [/tex] will lead to a fractional remainder when multiplying to get [tex] x^{4} [/tex].
