1. Factors, Prime Numbers & Composite Numbers

2. Definition Product – An answer to a multiplication problem. 7 x 8 = 56 Product

3. Definition Factor – a number that is multiplied by another to give a product. 7 x 8 = 56 Factors

4. Definition Factor – a number that divides evenly into another number. 56 ÷ 8 = 7 Factors

5. Test yourself… What are the factors and products? 1) 6 x 7 = 42 2) 63 ÷ 9 = 7 3) 8 x 5 = 40 Factors: 6 and 7 Product: 42 Factors: 7 and 9 Product: 63 Factors: 5 and 8 Product: 40

6. Example: 7 is prime because the only numbers that will divide into it evenly are 1 and 7. Definition Prime Number – a number that has only two factors, itself and 1.

7. Examples of Prime Numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…

8. 2345678910 11121314151617181920 21222324252627282930 31323334353637383940 41424344454647484950 51525354555657585960 61626364656667686970 71727374757677787980 81828384858687888990 919293949596979899100 Here’s How You Do It Take out numbers that have a composite factor of 2

9. 23579 1113151719 2123252729 3133353739 4143454749 5153555759 6163656769 7173757779 8183858789 9193959799 Here’s How You Do It Take out numbers that have a composite factor of 2

10. 23579 1113151719 2123252729 3133353739 4143454749 5153555759 6163656769 7173757779 8183858789 9193959799 Here’s How You Do It Take out numbers that have a composite factor of 3

11. 2357 11131719 232529 313537 41434749 535559 616567 71737779 838589 919597 Here’s How You Do It Take out numbers that have a composite factor of 3

12. 2357 11131719 232529 313537 41434749 535559 616567 71737779 838589 919597 Here’s How You Do It Take out numbers that have a composite factor of 5

13. 2357 11131719 2329 3137 41434749 5359 6167 71737779 8389 9197 Here’s How You Do It Take out numbers that have a composite factor of 5

14. 2357 11131719 2329 3137 41434749 5359 6167 71737779 8389 9197 Here’s How You Do It Take out numbers that have a composite factor of 7

15. 2357 11131719 2329 3137 414347 5359 6167 717379 8389 97 The PRIME Numbers! Take out numbers that have a composite factor of 7

16. Example: The number 8. The factors of 8 are 1, 2, 4, 8. Definition Composite number – a number that has more than two factors.

17. Examples of Composite Numbers 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, …

18. One is special because... One is not prime. (because it does not have exactly two different factors). One is not Composite. (because it does not have more than 2 factors).

19. Definition Prime Factorization – A way to write a composite number as the product of its prime factors. 2 x 2 x 3 = 12 or 22 22 x 3 = 12

20. How to do a Prime Factorization 48 Step 1 – Write down any composite number. - - Factor Tree Method - - Step 2 – Start dividing by the prime #s (start with 2). If the composite number is divisible by 2, write it down and find the next factor. If not, check if the factor is evenly divisible by 3, 5, 7, 9, etc. 2 x 24

21. How to do a Prime Factorization 48 Step 3 – Check the factors. If they are prime, you are done. If they are not, proceed to Step 4. - - Factor Tree Method - - Step 4 – Continue dividing. If one of the factors is divisible by 2, write it down and find the next factor. If not, check if the factor is evenly divisible by 3, 5, 7, 9, etc. 2 x 24 2 x 2 x 12

22. How to do a Prime Factorization 48 Step 5 – Check the factors. If they are prime, proceed to Step 6. If they are not, repeat Step 4. - - Factor Tree Method - - 2 x 24 2 x 2 x 12 2 x 2 x 2 x 6

23. How to do a Prime Factorization 48 Step 5 – Check the factors. If they are prime, proceed to Step 6. If they are not, repeat Step 4. - - Factor Tree Method - - Step 6 – Write the Prime Factorization in Exponential Form. 2 x 24 2 x 2 x 12 2 x 2 x 2 x 6 2 x 2 x 2 x 2 x 3 2 4 x 3 = 48

24. Find the Prime Factorization 4 2 x 2 2 2 = 4 Prime Factorization in Exponential Form

25. Find the Prime Factorization 6 2 x 3 = 6 Prime Factorization

26. Find the Prime Factorization 27 3 x 9 3 3 = 27 3 x 3 x 3 Prime Factorization in Exponential Form

27. Find the Prime Factorization 12 2 x 6 2 2 x 3 = 12 2 x 2 x 3 Prime Factorization in Exponential Form

28. Find the Prime Factorization 18 2 x 9 2 x 3 2 = 18 2 x 3 x 3 Prime Factorization in Exponential Form

29. You Have Options The following screens illustrate another method that you can use to find the Prime Factorization of a Composite Number. Try it! You may like it better.

30. How to do a Prime Factorization 18 Step 1 – Write down any composite number. - - Ladder Method - - Step 2 – Start dividing by the prime #s (start with 2). If the composite number is divisible by 2, write it on the left of the L and write the other factor below the original composite #. If not, check if the number is evenly divisible by 3, 5, etc. 2 9

31. How to do a Prime Factorization 18 Step 3 – Check the factors. If they are prime, proceed to Step 6. If not, continue the process. - - Ladder Method - - Step 4 – Continue dividing the # on the next rung of the ladder by the prime #s (start with 2). 2 93 3 Step 5 – Repeat this process until the # on the next rung of the ladder is prime. Prime #

32. How to do a Prime Factorization 18 - - Ladder Method - - 2 93 3 Prime Factorization 2 x 3 x 3 Prime Factorization in Exponential Form 2 x 3 2 Step 6 – Write the Prime Factorization in Exponential Form.

33. 56 - - Ladder Method - - 2 7 Prime Factorization 2 x 2 x 2 x 7 Prime Factorization in Exponential Form 2 3 x 7 282 142 Prime # Find the Prime Factorization

34. Summary One is not a prime or composite number. Two is the only even prime number. Not all odd numbers are prime. (examples: 9, 15, 21, 27, 33, 35, …) All composite numbers can be written as product of prime numbers.

35. The End