EXAMPLE 2 Identifying Prime and Composite Numbers

Write all the factors of the number and tell whether it is prime or composite.

a. 32

e. 149

b. 39

c. 43

d. 76

f. 121

1, 2, 4, 8, 16, 32

1, 3, 13, 39

1, 43

1, 2, 4, 19, 38, 76

1, 149

1, 11, 121

Number Factors Prime or Composite?

composite

composite

composite

composite

prime

prime

EXAMPLE 3 Writing Prime Factorization

Write the prime factorization of 450.

Three factor trees are shown. Notice that each factor tree produces the same prime factorization, differing only in the order of the factors.

So, 450 = 2 3 3 5 5.

EXAMPLE 3 Writing Prime Factorization

ANSWER

Using exponents, the prime factorization of 450 is 2 • 32 • 52

GUIDED PRACTICE for Examples 2 and 3

6. 24

Tell whether the number is prime or composite. If it is composite, write its prime factorization using exponents.

Composite; It has positive factors other then 1 and itself.

ANSWER

Using exponents, the prime factorization of 24 is 23 • 3

GUIDED PRACTICE for Examples 2 and 3

7. 51

Tell whether the number is prime or composite. If it is composite, write its prime factorization using exponents.

Composite; It has positive factors other then 1 and itself.

ANSWER

Using exponents, the prime factorization of 51 is 3 • 17

GUIDED PRACTICE for Examples 2 and 3

8. 73

Tell whether the number is prime or composite. If it is composite, write its prime factorization using exponents.

ANSWER

Prime; only positive factors are 1 and itself.

GUIDED PRACTICE for Examples 2 and 3

9. 560

Tell whether the number is prime or composite. If it is composite, write its prime factorization using exponents.

Composite; It has positive factors other then 1 and itself.

ANSWER

Using exponents, the prime factorization of 560 is 24 • 5 • 7