6th Grade Math Textbook, Progress

Prime Factorization

6-3

Every composite number can be written as the product of

prime factors. This is called prime factorization.

Find the prime factorization of 36.

You can use a factor tree to find the prime factors.


 Start with the composite number.


 Choose any2 factors.


 Continue factoring until all the

branches show primenumbers.


 Arrange the prime factors in order

from least to greatest. 2 
 2 
 3 
 3

The prime factorization of 36 is 2
 2 
 3 
3.

You can use exponents to express

the prime factorization of 36. 22 
 32

No matter which 2 factors you begin with,

the prime factorization will always be the same.

36

Composite.

Factor again.

3

3

3

3

3 2

12

4

(^2) All prime.
Remember:
2
2  22
3
3  32
36




Composite.
Factor again.
Composite.
Factor again.
22
32
2 3 2 3
6 6
36




22
32
2 2 3 3
4 9
Composite.
Factor again.
Express each in exponential form. Then find the product.

1. 5
   2
   2
   5 2. 2
   2
   2
   3 3. 11
   2
   11
   5


2. 7
   3
   2
   7
   3 5. 5
   13
   5
   5 6. 2
   7
   2
   7

Make a factor tree for each to find the prime factorization.

7. 45 8. 64 9. 72 10. 88 11. 48

Composite.

Factor again.

Composite.

Factor again.

Composite.

Factor again.

Composite.

Factor again.

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