1. 4.2 Factors and Prime Factorization
Learn to write prime factorizations of composite numbers.

2. Vocabulary
factor
prime factorization
Prime Number Brain Pop

3. Whole numbers that are multiplied to find a product are called factors of that product. A number is divisible by its factors. 2 3 = 6 6 ÷ 3 = 2
6 is divisible by 3 and 2. 6 ÷ 2 = 3
Factors
Product

4. Helpful Hint
When the pairs of factors begin to repeat, then you have found all of the factors of the number you are factoring.

5. Additional Example 1A: Finding Factors
List all of the factors of the number 16.
A. 16
16 = 1 • 16
1 is a factor.
16 = 2 • 8
2 is a factor.
3 is not a factor.
16 = 4 • 4
4 is a factor.
5 is not a factor.
6 is not a factor.
7 is not a factor.
16 = 8 • 2
8 and 2 have already been listed so stop here. 1 2 4 4 8 16
You can draw a diagram to illustrate the factor pairs.
The factors of 16 are 1, 2, 4, 8, and 16.

6. Additional Example 1B: Finding Factors
List all of the factors of the number 19.
B. 19
19 = 1 • 19
19 is not divisible by any other whole number.
The factors of 19 are 1 and 19.

7. You can use factors to write a number in different ways.
Factorization of 12
Notice that these factors are all prime.
1 • 12
2 • 6
3 • 4
3 • 2 • 2
Prime factorization A way to write a composite number as the product of prime factors.

8. Additional Example 2A: Writing Prime Factorizations
Write the prime factorization of 24.
Method 1: Use a factor tree.
Choose any two factors of 24 to begin. Keep finding factors until each branch ends at a prime factor. 24 24 • 6 • 2 12 4 2 • 6 3 • 2 2 • 2 2 • 3
24 = 3 • 2 • 2 • 2
24 = 2 • 2 • 2 • 3
The prime factorization of 24 is 2 • 2 • 2 • 3, or 23 • 3.

9. Write the prime factorization of 28.
Check It Out: Example 2A
Write the prime factorization of 28.
Method 1: Use a factor tree.
Choose any two factors of 28 to begin. Keep finding factors until each branch ends at a prime factor. 28 28 2 • 14 7 • 4 2 • 7 2 • 2
28 = 2 • 2 • 7
28 = 7 • 2 • 2
The prime factorization of 28 is 2 • 2 • 7, or 22 • 7 .

10. Prime factor this number12
3 x 4
= 12
3 x 2 x 2 = 12
2 x 2 x 3 = 12 2
2 x 3 = 12

11. Prime factor this number14
2 x 7
= 14

12. Prime factor this number18
3 x 6
= 18
3 x 2 x 3 = 18
2 x 3 x 3 = 18
2 x 3 = 18 2

13. Watch…….
Factoring Brain Pop