McGraw-Hill Education GRE 2019

240

120

3 5

2

2

60

2 30

2 15

The prime factorization of 240 is thus: (2^4 ) × 3 × 5. From Property 2 earlier, you can

infer that 40 is a factor of 240 but that 32 is not. Why? Because the prime factors

of 40 (2 × 2 × 2 × 5) are contained in the prime factorization of 240, but the prime

factors of 32 (2 × 2 × 2 × 2 × 2) are not contained in the prime factorization of 240.

One important principle that extends from the preceding explanation is the

following:

If a is a factor of b, and b is a factor of c, then a must be a factor of c.

For example, since 40 is a factor of 240, 8 and 5 (which are factors of 40) must also

be factors of 240.

Generally, when doing questions that concern divisibility, you should

focus on prime factorization.

If y is divisible by 12, which of the following must be true? Indicate all

that apply.

A y is divisible by 24

B y is divisible by 6

C y is divisible by 4

SOLUTION: If y is divisible by 12, then the prime factors of 12 must be prime

factors of y. Create a factor tree to determine the prime factors of 12.

12

4

22

12 = 2^2 × 3

3

CHAPTER 9 ■ NUMBER PROPERTIES 177

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