How do you find the GCF of 42x^242x2, 56x^356x3?

1 Answer
Oct 13, 2015

GCF(42x^2,56x^3)=14x^2GCF(42x2,56x3)=14x2

Explanation:

As for the numerical part:

GCF(42,56)=GCF(2*3*7, 2^3*7)GCF(42,56)=GCF(237,237)

The rule is to look for common primes, and take them with the smallest exponents. 22 is a common prime. It occours once as 22, then as 2^323. So, the one with the smallest exponent is 22. 33 is not a common prime, since it only divides 4242. 77 is a common prime, and it appears in both factorization as 77, so there's nothing to choose. The GCF is thus 2*7=1427=14

For the variables, it is easier: x^2x2 divides x^3x3, so GCF(x^2,x^3)=x^2GCF(x2,x3)=x2.