Question

How do you find the GCF of `42x^2`, `56x^3`?

Answer 1

`GCF(42x^2,56x^3)=14x^2`

Explanation:

As for the numerical part:

`GCF(42,56)=GCF(2*3*7, 2^3*7)`

The rule is to look for common primes, and take them with the smallest exponents. `2` is a common prime. It occours once as `2`, then as `2^3`. So, the one with the smallest exponent is `2`. `3` is not a common prime, since it only divides `42`. `7` is a common prime, and it appears in both factorization as `7`, so there's nothing to choose. The GCF is thus `2*7=14`

For the variables, it is easier: `x^2` divides `x^3`, so `GCF(x^2,x^3)=x^2`.