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

1 Answer
KillerBunny
Oct 13, 2015

#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#.

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