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

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Answer 1 · 2017-02-12T15:01:19

See the entire solution process below:

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#