1. Multiplying and Dividing Fractions
Chapter 2
Multiplying and Dividing Fractions

2. Factors and Prime Factorization
2.2
Factors and Prime Factorization

3. Finding the Factors of Numbers
To perform many operations, it is necessary to be able to factor a number.
Since 7 · 9 = 63, both 7 and 9 are factors of 63, and 7 · 9 is called a factorization of 63.
Objective A 3

4. Prime and Composite Numbers
Prime Numbers
A prime number is a natural number that has exactly two different factors 1 and itself.
Composite Numbers
A composite number is any natural number, other than 1, that is not prime.
Objective A 4

5. Examples
Determine whether each number is prime or composite. Explain your answers.
a. 16
b. 31
c. 49
Composite, it has more than two factors: 1, 2, 4, 8, 16.
Prime, its only factors are 1 and 31.
Objective A
Composite, it has more than two factors: 1, 7, 49. 5

6. Prime Factorization Prime Factorization
The prime factorization of a number is the factorization in which all the factors are prime numbers.
Every whole number greater than 1 has exactly one prime factorization.
Objective A 6

7. Examples Find the prime factorization of 63.
The first prime number 2 does not divide evenly, but 3 does.
Because 21 is not prime, we divide again.
The quotient 7 is prime, so we are finished. The prime factorization of 63 is 3 · 3 · 7.
Objective A 7

8. Divisibility Tests
Objective A 8

9. Factor Trees
Another way to find the prime factorization is to use a factor tree.
Objective A 9

10. Examples Find the prime factorization of 30.
Write 30 as the product of two numbers. Continue until all factors are prime. 30 •
3 • • 5
The prime factorization of 30 is 2 · 3 · 5.
Objective A 10

11. Examples Find the prime factorization of 36.
Write 36 as the product of two numbers. Continue until all factors are prime. 36 •
3 • • 2
The prime factorization of 36 is 3 · 3 · 2 · 2 or 32 · 22.
Objective A 11