Prime Factorization (Factor Trees)

# Prime Factorization (Factor Trees)

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## Prime Factorization (Factor Trees)

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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: • Find two factors of the given number (except1) • HINT: Use divisibility rules and/or start with 2 24 2x12

4. 24 2x12 • Step 2: • Check if those new numbers are composite or prime PRIME COMPOSITE

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

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

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

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

9. Prime Factorization • Step 1: • Find two factors of the given number (except 1) • HINT: Use divisibility rules and/or start with 2 36 2x18

10. 36 2x18 • Step 2: • Check if those new numbers are composite or prime PRIME COMPOSITE

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

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

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

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

15. Prime Factorization • Step 1: • Find two factors of the given number (except 1) • HINT: Use divisibility rules and/or start with 2 36 4x9

16. 36 4x9 • Step 2: • Check if those new numbers are composite or prime COMPOSITE COMPOSITE

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

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

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

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

21. Prime Factorization • Step 1: • Find two factors of the given number (except 1) • HINT: Use divisibility rules and/or start with 2 36 3x12

22. 36 3x12 • Step 2: • Check if those new numbers are composite or prime PRIME COMPOSITE

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

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

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

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