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Prime Factorization(Factor Trees)

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)

Prime Factorization

- Step 1
- Find two factors of the given number (except1)
- HINT Use divisibility rules and/or start with 2

24

2 x 12

- Step 2
- Check if those new numbers are composite or

prime

PRIME

COMPOSITE

- 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

- Step 4
- Repeat until all numbers are prime

2 x 3

- Step 5
- Rewrite into a sentence

The prime factors of 24 are 2 x 2 x 2 x 3.

- To Check
- Multiply the prime factors together, you should

end up with the original number

2 x 2 x 2 x 3

Prime Factorization

- Step 1
- Find two factors of the given number (except 1)
- HINT Use divisibility rules and/or start with 2

36

2 x 18

- Step 2
- Check if those new numbers are composite or

prime

PRIME

COMPOSITE

- 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

- Step 4
- Repeat until all numbers are prime

3 x 3

- Step 5
- Rewrite into a sentence

The prime factors of 36 are 2 x 2 x 3 x 3.

- To Check
- Multiply the prime factors together, you should

end up with the original number

2 x 2 x 3 x 3

Prime Factorization

- Step 1
- Find two factors of the given number (except 1)
- HINT Use divisibility rules and/or start with 2

36

4 x 9

- Step 2
- Check if those new numbers are composite or

prime

COMPOSITE

COMPOSITE

- Step 3
- For each new number
- If it is prime, stop
- If it is composite, find two more factors of the

new number

3 x 3

2 x 2

x

- Step 4
- Repeat until all numbers are prime

- Step 5
- Rewrite into a sentence

The prime factors of 36 are 2 x 2 x 3 x 3.

- To Check
- Multiply the prime factors together, you should

end up with the original number

2 x 2 x 3 x 3

Prime Factorization

- Step 1
- Find two factors of the given number (except 1)
- HINT Use divisibility rules and/or start with 2

36

3 x 12

- Step 2
- Check if those new numbers are composite or

prime

PRIME

COMPOSITE

- 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

- Step 4
- Repeat until all numbers are prime

2 x 3

- Step 5
- Rewrite into a sentence

The prime factors of 36 are 2 x 2 x 3 x 3.

- To Check
- Multiply the prime factors together, you should

end up with the original number

2 x 2 x 3 x 3

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