Practice Math Questions for Praxis: Finding the Greatest Common Factor

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

1. What is the greatest common factor of 35a⁴b⁷c¹² and 20a⁸b³c¹⁰?

   A. 7a⁴b³c¹⁰ B. 5a⁴b⁷c¹² C. 10a⁴b³c¹⁰ D. 5a⁴b³c¹⁰ E. 10a⁸b⁸c¹²

2. 6xy is the greatest common factor of 24x²y and which of the following terms?

   A. 8xy B. 12x C. 24y D. 42xy² E. 3x²y

Answers and explanations

1. 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 5a⁴b³c¹⁰.
2. The correct answer is Choice (D). The first thing to look for is which choices have 6xy for a factor. 6xy must be a factor of a term to be a greatest common factor of it and 24x²y. 6xy is not a factor of Choice (A) because 6 isn’t a factor of 8, and 6xy isn’t a factor of Choice (B) because y does not go into 12x. 6xy is also not a factor of Choice (C) because x doesn’t go into 24y. And 6xy 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. 6xy is a factor of 42xy². 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 24x²y and 42xy², 6xy is the greatest common factor of 24xy² and 42xy².