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

Mar 20, 2018

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

#### Explanation:

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

GCF is the greatest common factor.

$64 {x}^{8} {y}^{3} = \textcolor{red}{2 \cdot 2 \cdot 2} \cdot 2 \cdot 2 \cdot 2 \cdot \textcolor{red}{x \cdot x \cdot x \cdot x \cdot x \cdot x} \cdot x \cdot x \cdot \textcolor{red}{y \cdot y \cdot y}$

$40 {x}^{6} {y}^{8} = \textcolor{red}{2 \cdot 2 \cdot 2} \cdot 5 \cdot \textcolor{red}{x \cdot x \cdot x \cdot x \cdot x \cdot x} \cdot \textcolor{red}{y \cdot y \cdot y} \cdot y \cdot y \cdot y \cdot y \cdot y$

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

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

x^8 = x^6x^2; " "y^8 = y^3y^5

So,
$64 {x}^{8} {y}^{3} = \textcolor{red}{8} \cdot 8 \textcolor{red}{{x}^{6}} {x}^{2} \textcolor{red}{{y}^{3}}$

$40 {x}^{6} {y}^{8} = \textcolor{red}{8} \cdot 5 \textcolor{red}{{x}^{6}} \textcolor{red}{{y}^{3}} {y}^{5}$

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