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.