In the following practice questions, you first have to find the GCF of two terms, and then find one of the original terms, given the GCF and the other original term.

## Practice questions

- What is the greatest common factor of 35
*a*^{4}*b*^{7}*c*^{12}and 20*a*^{8}*b*^{3}*c*^{10}?**A.**7*a*^{4}*b*^{3}*c*^{10}**B.**5*a*^{4}*b*^{7}*c*^{12}**C.**10*a*^{4}*b*^{3}*c*^{10}**D.**5*a*^{4}*b*^{3}*c*^{10}**E.**10*a*^{8}*b*^{8}*c*^{12} - 6
*xy*is the greatest common factor of 24*x*^{2}*y*and which of the following terms?**A.**8*xy***B.**12*x***C.**24*y***D.**42*xy*^{2}**E.**3*x*^{2}*y*

## Answers and explanations

- The correct answer is Choice
**(D).**To find the greatest common factor of the two terms, find the greatest common factor of the coefficients and write it next to each common variable. Give each common variable the lowest exponent it has in the terms. The greatest common factor of 35 and 20 is 5, the lowest exponent of*a*in the terms is 4, the lowest exponent of*b*is 3, and the lowest exponent of*c*is 10. Thus, the greatest common factor of the two terms is 5*a*^{4}*b*^{3}*c*^{10}. - The correct answer is Choice
**(D).**The first thing to look for is which choices have 6*xy*for a factor. 6*xy*must be a factor of a term to be a greatest common factor of it and 24*x*^{2}*y*. 6*xy*is not a factor of Choice (A) because 6 isn’t a factor of 8, and 6*xy*isn’t a factor of Choice (B) because*y*does not go into 12*x.*6*xy*is also not a factor of Choice (C) because*x*doesn’t go into 24*y*. And 6*xy*isn’t a factor of Choice (E) because 6 isn’t a factor of 3.Alternatively, you can eliminate Choices (A) and (E) because their coefficients, 8 and 3, aren’t multiples of 6. And you can eliminate Choices (B) and (C) because the correct answer needs both an

*x*and a*y.*That leaves Choice (D) to consider. 6*xy*is a factor of 42*xy*^{2}. Because 6 is the greatest common factor of 24 and 42, and because*x*has a lowest exponent of 1 and*y*has a lowest exponent of 1 in 24*x*^{2}*y*and 42*xy*^{2}, 6*xy*is the greatest common factor of 24*xy*^{2}and 42*xy*^{2}.