McGraw-Hill Education GRE 2019

You can therefore infer that y has 2, 2, and 3 in its prime factorization. Since y has

2 × 2 in its prime factorization, y must be divisible by 4. Since y has 2 × 3 in its

prime factorization, y must be divisible by 6. The correct answer is B and C.

Greatest Common Factor and Least Common Multiple

The greatest common factor (GCF) of a set of numbers is the largest integer that

divides evenly into all the numbers. To determine the greatest prime factor of a set

of numbers, break each of the numbers down into their prime factors and circle the

shared factors. The product of the shared factors will be the GCF.

For this question, write your answer in the box.

What is the greatest common factor of 12, 72, and 88?

SOLUTION: Determine the prime factors of each of the numbers and circle

their common prime factors:

12

3

72

6

2

12

334

2 2

88

8

4

11

2

2 2

4

2 2

12, 72, and 88 each have two 2s in their prime factorizations. The GCF of the three

numbers is thus 2 × 2 = 4.

The least common multiple (LCM) of a set of numbers is the smallest integer

that is divisible by all the numbers in the set. The LCM must therefore contain the

prime factors of each number in the set. As with the GCF, prime factorization is

important for LCM questions.

If x is the smallest integer that is divisible by 9, 12, and 15, what is the value

of x?

SOLUTION: You are asked to determine the LCM of 9, 12, and 15. First, break

each number down into its prime factorization:

9

33

15

35

12

4

2

3

2

178 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 178 12/05/17 11:51 am