Section 5.1

Prime Factorization

and

Greatest Common Factor

A prime number is a number that can only be divided by

only one and itself.

A composite number is a number greater than one that is not prime.

Prime or composite?37

prime51

composite

Prime or Composite?89

1. Prime

2. Composite

3. Both

4. Neither

1) Find the prime factorization of 84.84 = 4 • 21

= 2 • 2 • 3 • 7

= 22 • 3 • 7

2) Find the prime factorization of -210.

-210 = -1 • 210

= -1 • 30 • 7

= -1 • 6 • 5 • 7

= -1 • 2 • 3 • 5 • 7

3) Find the prime factorization of 45a2b3

45a2b3 = 9 • 5 • a • a • b • b • b

= 3 • 3 • 5 • a • a • b • b • b

= 32 • 5 • a • a • b • b • b

Write the variables without exponents.

What is the prime factorization of 48?

1. 3 16

2. 3 4 4

3. 2 2 3 4

4. 2 2 2 2 3

The Greatest Common Factor (GCF) of 2 or more numbers isthe largest number that can divide

into all of the numbers.

4) Find the GCF of 42 and 60.

Write the prime factorization of each number.

4) Find the GCF of 42 and 60.

What prime factors do the numbers have in common?

Multiply those numbers.

The GCF is 2 • 3 = 6

6 is the largest number that can go into 42 and 60!

42 = 2 •  3 • 760 = 2 • 2 • 3 • 5

5) Find the GCF of 40a2b and 48ab4.

40a2b = 2 • 2 • 2 • 5 • a • a • b48ab4 = 2 • 2 • 2 • 2 • 3 • a • b • b • b • b

What do they have in common?Multiply the factors together.

GCF = 8ab

What is the GCF of 48 and 64?

1. 2

2. 4

3. 8

4. 16

What is the GCF of?

• 36 and 60

• 28a and 35a2

• 45 and 75

Some to try:

• 8ab and 48a

• 28, 42, 56

• 50, 55, 60