How do you find the GCF of $64 x^{8} y^{3}$ $64x^8y^3$ , $40 x^{6} y^{8}$ $40x^6y^8$ ?

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How do you find the GCF of $64 x^{8} y^{3}$ $64x^8y^3$ , $40 x^{6} y^{8}$ $40x^6y^8$ ?

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Answer 1 · 2018-03-20T05:19:25

GCF $= 8 x^{6} y^{3}$ $= 8x^6y^3$

Explanation:

Given: Find GCF of $64 x^{8} y^{3} and 40 x^{6} y^{8}$ $64x^8y^3 " and " 40x^6y^8$

GCF is the greatest common factor.

$64 x^{8} y^{3} = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y$ $64x^8y^3 = color(red)(2*2*2)*2*2*2*color(red)(x*x*x*x*x*x)*x*x*color(red)(y*y*y)$

$40 x^{6} y^{8} = 2 \cdot 2 \cdot 2 \cdot 5 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y$ $40x^6y^8 = color(red)(2*2*2)*5*color(red)(x*x*x*x*x*x)*color(red)(y*y*y)*y*y*y*y*y$

The GCF = $2 \cdot 2 \cdot 2 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y = 8 x^{6} y^{3}$ $2*2*2*x*x*x*x*x*x*y*y*y = 8x^6y^3$

A simpler way to find the GCF use the exponent rule: $x^{m} x^{n} = x^{m + n}$ $x^mx^n = x^(m+n)$

$x^{8} = x^{6} x^{2}; y^{8} = y^{3} y^{5}$ $x^8 = x^6x^2; " "y^8 = y^3y^5$

So,
$64 x^{8} y^{3} = 8 \cdot 8 x^{6} x^{2} y^{3}$ $64x^8y^3 = color(red)(8)*8color(red)(x^6)x^2color(red)(y^3)$

$40 x^{6} y^{8} = 8 \cdot 5 x^{6} y^{3} y^{5}$ $40x^6y^8 = color(red)(8)*5color(red)(x^6)color(red)(y^3)y^5$

GCF = $8 x^{6} y^{3}$ $8x^6y^3$

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How do you find the GCF of $64 x^{8} y^{3}$ $64x^8y^3$ , $40 x^{6} y^{8}$ $40x^6y^8$ ?

1 Answer

Explanation:

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How do you find the GCF of $64 x^{8} y^{3}$ $64x^8y^3$ , $40 x^{6} y^{8}$ $40x^6y^8$ ?