TRUE/FALSE The greatest common factor of 56f 3g 2 and 70fg 3 is 7fg 3.

Question

The greatest common factor of 56f ³g ² and 70fg ³ is 7fg ³.

True

False

 

Answer 1

trueeeeeeeeee

Answer 2

Two algebraic terms given: 56f³g² and 70fg³

First, factor the numerical coefficient of each term using the prime factorization:

56=2x28=2x2x14=2x2x2x7 and 70=2x35=2x5x7

Both coefficients have one "2" and one "7" in common.

So, the GCF, the greatest common factor, of 56 and 70 is: GCF=2x7=14 ··· (1)

Then, factor the variables of each term in the same manner shown above:

f³g²=fxfxfxgxg and fg³=fxgxgxg

Both variables have one "f" and two "g"s in common.

So, the GCF of f³g² and fg³ is: GCF=fxgxg=fg² ··· (2)

Thus, the GCF of two algebraic terms is: GCF=(1)x(2)=14fg²

Therfore, "7fg³" is false.   The right answer is 14fg².