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Prime Factorization (Factor Trees)
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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)
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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
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Step 2: 24 2 x 12 Check if those new numbers are composite or prime
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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
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Step 4: Repeat until all numbers are prime 24 2 x 12 2 x 6 x x 2 x 3
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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.
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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
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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
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Step 2: 36 2 x 18 Check if those new numbers are composite or prime
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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
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Step 4: Repeat until all numbers are prime 36 2 x 18 2 x 9 x x 3 x
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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.
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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
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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
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Step 2: 36 4 x 9 Check if those new numbers are composite or prime
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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
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Step 4: Repeat until all numbers are prime 36 4 x 9 3 x 3 2 x 2 x
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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.
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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
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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
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Step 2: 36 3 x 12 Check if those new numbers are composite or prime
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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
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Step 4: Repeat until all numbers are prime 36 3 x 12 2 x 6 x x x 2 x
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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.
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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
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