EXAMPLE 2 Identifying Relatively Prime Numbers

Tell whether the numbers 112 and 45 are relatively prime.

SOLUTION

Write the prime factorization of each number. Then look for all the common prime factors.

112 = 24 7 45 = 32 5

There are no common prime factors. However, two numbers always have 1 as a common factor. So, the GCF is 1.

EXAMPLE 2 Identifying Relatively Prime Numbers

ANSWER

The numbers 112 and 45 are relatively prime.

EXAMPLE 3 Solve a Multi-Step Problem

Pep Rally

Students at your school are planning to hand out pep rally packs to support your school’s athletic program. The students have 240 bumper stickers, 360 pennants, and 720 pencils. Every pack must have the same contents, and no items should be left over. What is the greatest number of packs that can be made? What will each pack contain?

EXAMPLE 3 Solve a Multi-Step Problem

STEP 1

Find the greatest number of pep rally packs by finding the GCF.

240 = 24 3 5 720 = 24 32 5360 = 23 32 5

The common prime factors are 23, 3 and 5. The GCF is 23 3 5, or 120. So, 120 pep rally packs can be made.

EXAMPLE 3 Solve a Multi-Step Problem

STEP 2

Divide the number of items by the number of pep rally packs.

ANSWER

The greatest number of pep rally packs is 120. Each pack will contain 2 bumper stickers, 3 pennants, and 6 pencils.

240 120 = 2 360 120 = 3 720 120 = 6

GUIDED PRACTICE for Examples 2 and 3

Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF.

5. 48, 72

GUIDED PRACTICE for Examples 2 and 3

ANSWER

The number 48 and 72 are not relatively prime. The GCF is 23 3, or 24

GUIDED PRACTICE for Examples 2 and 3

Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF.

6. 124, 128

GUIDED PRACTICE for Examples 2 and 3

ANSWER

The numbers 124 and 128 are not relatively prime. The GFC is 22 or 4

GUIDED PRACTICE for Examples 2 and 3

Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF.

7. 39, 44

GUIDED PRACTICE for Examples 2 and 3

ANSWER

The numbers 39 and 44 are relatively prime.

GUIDED PRACTICE for Examples 2 and 3

Tell whether the numbers are relatively prime. If they are not relatively prime, find the GCF.

8. 200, 63

GUIDED PRACTICE for Examples 2 and 3

ANSWER

The numbers 200 and 63 are relatively prime.

GUIDED PRACTICE for Examples 2 and 3

9. What If? In Example 3, suppose the students have 240 bumper stickers and 360 pennants, but only 600 pencils. How many pep rally packs can be made? What items will each pack contain?

ANSWER

The greatest number of pep rally packs is 120. Each pack will contain 2 bumper stickers, 3 pennants, and 6 pencils.