How do you find the GCF of $42 x^{2}$ $42x^2$ , $56 x^{3}$ $56x^3$ ?

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How do you find the GCF of $42 x^{2}$ $42x^2$ , $56 x^{3}$ $56x^3$ ?

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Answer 1 · 2015-10-13T20:38:02

$G C F (42 x^{2}, 56 x^{3}) = 14 x^{2}$ $GCF(42x^2,56x^3)=14x^2$

Explanation:

As for the numerical part:

$G C F (42, 56) = G C F (2 \cdot 3 \cdot 7, 2^{3} \cdot 7)$ $GCF(42,56)=GCF(2*3*7, 2^3*7)$

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

For the variables, it is easier: $x^{2}$ $x^2$ divides $x^{3}$ $x^3$ , so $G C F (x^{2}, x^{3}) = x^{2}$ $GCF(x^2,x^3)=x^2$ .

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How do you find the GCF of $42 x^{2}$ $42x^2$ , $56 x^{3}$ $56x^3$ ?

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