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Prime Factorization (Factor Trees)

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Presentation on theme: "Prime Factorization (Factor Trees)"— Presentation transcript:

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


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