1. Prime Factorization (Factor Trees)

2. Prime Factorization
Any composite number can be written as a product of prime numbers
This is done by a process called prime factorization (factor trees)

3. Prime Factorization Step 1: 24 2 x 12
Find two factors of the given number (except1)
HINT: Use divisibility rules and/or start with 2 24
2 x 12

4. Step 2: 24 2 x 12 Check if those new numbers are composite or prime

5. Step 3: 24 2 x 12 2 x 2 x 6 For each new number: If it is prime, stop
If it is composite, find two more factors of the new number 24
2 x 12 x
2 x 6

6. Step 4:
Repeat until all numbers are prime 24
2 x 12
2 x 6 x x
2 x 3

7. Step 5: 24 2 x 12 2 x 2 x 6 2 x 2 x 3 Rewrite into a sentence
The prime factors of 24 are 2 x 2 x 2 x 3.

8. To Check:
Multiply the prime factors together, you should end up with the original number 24
2 x 12
2 x 6
2 x 3 x x
2 x 2 x 2 x 3 = 24

9. Prime Factorization Step 1: 36 2 x 18
Find two factors of the given number (except 1)
HINT: Use divisibility rules and/or start with 2 36
2 x 18

10. Step 2: 36 2 x 18 Check if those new numbers are composite or prime

11. Step 3: 36 2 x 18 2 x 2 x 9 For each new number: If it is prime, stop
If it is composite, find two more factors of the new number 36
2 x 18 x
2 x 9

12. Step 4:
Repeat until all numbers are prime 36
2 x 18
2 x 9 x x
3 x

13. Step 5: 36 2 x 18 2 x 2 x 9 3 x 3 Rewrite into a sentence
The prime factors of 36 are 2 x 2 x 3 x 3.

14. To Check:
Multiply the prime factors together, you should end up with the original number 36
2 x 18
2 x 9 x
3 x
2 x 2 x 3 x 3 = 36

15. Prime Factorization Step 1: 36 4 x 9
Find two factors of the given number (except 1)
HINT: Use divisibility rules and/or start with 2 36
4 x 9

16. Step 2: 36 4 x 9 Check if those new numbers are composite or prime

17. Step 3: 36 4 x 9 2 x 2 x 3 x 3 For each new number:
If it is prime, stop
If it is composite, find two more factors of the new number 36
4 x 9
2 x 2 x
3 x 3

18. Step 4:
Repeat until all numbers are prime 36
4 x 9
3 x 3
2 x 2 x

19. Step 5: 36 4 x 9 3 x 3 2 x 2 x Rewrite into a sentence
The prime factors of 36 are 2 x 2 x 3 x 3.

20. To Check:
Multiply the prime factors together, you should end up with the original number 36
4 x 9
3 x 3
2 x 2 x
2 x 2 x 3 x 3 = 36

21. Prime Factorization Step 1: 36 3 x 12
Find two factors of the given number (except 1)
HINT: Use divisibility rules and/or start with 2 36
3 x 12

22. Step 2: 36 3 x 12 Check if those new numbers are composite or prime

23. Step 3: 36 3 x 12 3 x 2 x 6 For each new number: If it is prime, stop
If it is composite, find two more factors of the new number 36
3 x 12 x
2 x 6

24. Step 4:
Repeat until all numbers are prime 36
3 x 12
2 x 6 x x x
2 x

25. Step 5: 36 3 x 12 2 x 6 3 x 2 x 3 2 x Rewrite into a sentence
The prime factors of 36 are 2 x 2 x 3 x 3.

26. To Check:
Multiply the prime factors together, you should end up with the original number 36
3 x 12
2 x 6 x
2 x x
2 x 2 x 3 x 3 = 36