McGraw-Hill Education GRE 2019

The multiples of an integer are the products that result when that integer is

multiplied by another integer. For example, the multiples of 12 are 12(1) =

12, 12(2) = 24, 12(3) = 36,....

Note that multiples and factors are essentially opposites of each other.

Since 6 is a factor of 24, 24 is a multiple of 6.

The GRE expresses the preceding relationships in several ways. All of the following

sentences mean the same thing:

2 is a factor of 12 12 is a multiple of 2

2 is a divisor of 12 12 is divisible by 2

2 divides evenly into 12 12 divided by 2 yields an integer

Many test-takers tend to confuse factors and multiples. If this is the case, think to

yourself that there are finite factors and many multiples. The factors are what create

a number and the multiples are what result from that number.

Prime Factors and the Factor Tree

Any number will always have 1 and itself as divisors. If an integer is divisible only

by 1 and itself, then it is a prime number. Examples of prime numbers are 2, 3, 5, 7,

11, 13, and so on.

1 is not a prime number, and 2 is the only even prime number!

A prime factor is any factor of an integer that is also prime. For example, 2 and

3 are prime factors of 12, but 4 is not. There are two important properties about

prime factors:

1. Any integer can be expressed as the product of its prime factors. For example:
   12 = 2 × 2 × 3.


2. The factors of any integer will be completely determined by the prime factors
   of that integer. For example, 12 = 2 × 2 × 3. The factors of 12 are 1, 2, 3, (2 × 2),
   (2 × 3), (2 × 2 × 3).

To determine the prime factors of a number, you should create a factor tree. The

following is the factor tree for 240.

176 PART 4 ■ MATH REVIEW

03-GRE-Test-2018_173-312.indd 176 12/05/17 11:51 am