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
24
2
PRIME
x
12
COMPOSITE

Step 3:
• For each new number:
• If it is prime, stop
• If it is composite, find two more factors of the new
number
24
2
2
x
x
2
12
x
6

Step 4:
• Repeat until all numbers are prime
24
2
2
2
x
x
x
2
12
2
x
x
2
6
x
3

Step 5:
• Rewrite into a sentence
24
2
2
2
x
x
x
2
12
2
x
x
2
6
x
3
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
24
2
2
2
x
x
x
2
12
2
x
x
2
2 x 2 x 2 x 3 = 24
6
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
36
2
PRIME
x
18
COMPOSITE

Step 3:
• For each new number:
• If it is prime, stop
• If it is composite, find two more factors of the new
number
36
2
2
x
x
2
18
x
9

Step 4:
• Repeat until all numbers are prime
36
2
2
2
x
2
x
x
18
2
x
x
3
9
x
3

Step 5:
• Rewrite into a sentence
36
2
2
2
x
2
x
x
18
2
x
x
3
9
x
3
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
36
2
2
2
x
2
x
x
18
2
x
x
3
2 x 2 x 3 x 3 = 36
9
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
36
4
COMPOSITE
x
9
COMPOSITE

Step 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

Step 4:
• Repeat until all numbers are prime
36
4
x
9
2 x 2 x 3 x 3

Step 5:
• Rewrite into a sentence
36
4
x
9
2 x 2 x 3 x 3
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
36
4
x
9
2 x 2 x 3 x 3
2 x 2 x 3 x 3 = 36
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
36
3
PRIME
x
12
COMPOSITE

Step 3:
• For each new number:
• If it is prime, stop
• If it is composite, find two more factors of the new
number
36
3
3
x
x
2
12
x
6

Step 4:
• Repeat until all numbers are prime
36
3
3
3
x
2
x
x
12
2
x
x
2
6
x
3

Step 5:
• Rewrite into a sentence
36
3
3
3
x
2
x
x
12
2
x
x
2
6
x
3
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
36
3
3
3
x
2
x
x
12
2
x
x
2
2 x 2 x 3 x 3 = 36
6
x
3