How do you find the greatest common factor for the list of terms 70x^2, 30x^6, 60x^970x2,30x6,60x9?

1 Answer
smendyka
Feb 12, 2017

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 x70x2=2×5×7×x×x

30x^6 = 2 xx 5 xx 3 xx x xx x xx x xx x xx x xx x30x6=2×5×3×x×x×x×x×x×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 x90x9=2×5×3×3×x×x×x×x×x×x×x×x×x

The Common Factors are:

70x^2 = color(red)(2 xx 5) xx 7 xx color(red)(x xx x)70x2=2×5×7×x×x

30x^6 = color(red)(2 xx 5) xx 3 xx color(red)(x xx x) xx x xx x xx x xx x30x6=2×5×3×x×x×x×x×x×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 x90x9=2×5×3×3×x×x×x×x×x×x×x×x×x

Therefore the GCG (Greatest Common Factor) is:

color(red)(2 xx 5 xx) color(red)(x xx x) = 10x^22×5×x×x=10x2

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