Question

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

Answer 1

GCF `= 8x^6y^3`

Explanation:

Given: Find GCF of `64x^8y^3 " and " 40x^6y^8`

GCF is the greatest common factor.

`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)`

`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*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^mx^n = x^(m+n)`

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

So,
`64x^8y^3 = color(red)(8)*8color(red)(x^6)x^2color(red)(y^3)`

`40x^6y^8 = color(red)(8)*5color(red)(x^6)color(red)(y^3)y^5`

GCF = `8x^6y^3`