Question

find the greatest common factor of the following monomials: 44b^5 36b ?

Answer 1

GCF problems make you look at factors common to both monomials. If we factored each out completely, that would help in finding the common factors:

For 36b^2, the factors are 2, 2, 3, 3, b, b
For 54b^4, the factors are 2, 3, 3, 3, b, b, b, b

The common factors are 2, 3, 3, b, b - if they show up in both lists, cross them out and list them separately like we did here. The GCF, then, comes from these factors multiplied out, or 18b^2.

Use the same methodology for the second problem:

For 42x^2, the factors are 2, 3, 7, x, x
For 56x^3, the factors are 2, 2, 2, 7, x, x, x

Common factors are 2, 7, x, x. The GCF is then 14x^2.