1. EXAMPLE 2
Identifying Prime and Composite Numbers
Write all the factors of the number and tell whether it is prime or composite.
Number
Factors
Prime or Composite? a
1, 2, 4, 8, 16, 32
composite b
1, 3, 13, 39
composite c
1, 43
prime d
1, 2, 4, 19, 38, 76
composite e
1, 149
prime f
1, 11, 121
composite

2. 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 =

3. EXAMPLE 3
Writing Prime Factorization
ANSWER
Using exponents, the prime factorization of 450 is 2 • 32 • 52

4. 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

5. 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

6. 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.

7. 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 • 5 • 7