Question

How do you find the greatest common factor for the list of terms `70x^2, 30x^6, 60x^9`?

Answer 1

See the entire solution process below:

Explanation:

To find the Greatest Common Factor of these three terms we must first factor each term separately:

`70x^2 = 2 xx 5 xx 7 xx x xx x`

`30x^6 = 2 xx 5 xx 3 xx x xx x xx x xx x xx x xx x`

`90x^9 = 2 xx 5 xx 3 xx 3 xx x xx x xx x xx x xx x xx x xx x xx x xx x`

The Common Factors are:

`70x^2 = color(red)(2 xx 5) xx 7 xx color(red)(x xx x)`

`30x^6 = color(red)(2 xx 5) xx 3 xx color(red)(x xx x) xx x xx x xx x xx x`

`90x^9 = color(red)(2 xx 5) xx 3 xx 3 xx color(red)(x xx x) xx x xx x xx x xx x xx x xx x xx x`

Therefore the GCG (Greatest Common Factor) is:

`color(red)(2 xx 5 xx) color(red)(x xx x) = 10x^2`