# How do you find the greatest common factor of 80x^3, 30yx^2?

Mar 10, 2018

$g c f = 10 {x}^{2}$

#### Explanation:

Find the prime factorization of each of the given numbers:

$80 {x}^{3} = 16 \cdot 5 = {2}^{4} \cdot 5 \cdot {x}^{3}$
$30 y {x}^{2} = 2 \cdot 3 \cdot 5 \cdot y \cdot {x}^{2}$

the greatest common factor is the product of all common factors taken one at a time at the lowest exponent:

$g c f = 2 \cdot 5 \cdot {x}^{2} = 10 {x}^{2}$