1. Factors, Primes & Composite Numbers

2. Definition Product 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.
56 ÷ 8 = 7
Factor

5. What are the factors?
6 x 7 = 42
6 & 7
7 x 9 = 63
7 & 9
8 x 6 = 48
8 & 6
4 & 9
4 x 9 = 36

6. What are the factors?
42 ÷ 7 = 6 7
63 ÷ 9 = 7 9
48 ÷ 6 = 8 6 9
36 ÷ 9 = 4

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

8. Examples of Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19
Special Note:
One is not a prime number.

9. 8 Definition The factors of 8 are 1, 2, 4, 8
Composite number – a number that has more than two factors. 8
The factors of 8 are 1, 2, 4, 8

10. Examples of Composite Numbers
4, 6, 8, 9, 10, 12, 14, 15
Special Note:
Every whole number from 2 on is
either composite or prime.

11. Our Lonely 1 One is not a prime nor a composite number.
It is not prime
because it does
not have exactly
two different
factors.
It is not
composite
because it does
not have more
than 2 factors.
Special Note:
One is not a prime nor
a composite number.

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

13. How to Do Prime Factorization Using a Factor Tree
Step 1 – Start with a composite number. 48
Step 2 – Write down a multiplication
problem that equals this number or
any pair of factors of this number.
6 x 8 = 48

14. How to Do Prime Factorization Using a Factor Tree
Step 3 – Find factors of these factors.
6 x 8 = 48
2 x 3 x 2 x 4 = 48

15. How to Do Prime Factorization Using a Factor Tree
Step 4 – Find factors of these numbers
until all factors are prime numbers.
6 x 8 = 48
2 x 3 x 2 x 4 = 48
2 x 3 x 2 x 2 x 2 = 48

16. How to Do Prime Factorization Using a Factor Tree
Step 5 – Write the numbers from least
to greatest.
6 x 8 = 48
2 x 3 x 2 x 2 x 2 = 48
2 x 2 x 2 x 2 x 3 = 48

17. How to Do Prime Factorization Using a Factor Tree
Step 6 – Count how many numbers are
the same and write exponents for them.
6 x 8 = 48
2 x 3 x 2 x 2 x 2 = 48
2 x 2 x 2 x 2 x 3 = 48 4
2 x 3 = 48

18. Prime factor this number4
2 x 2
= 4 2
2 = 4

19. Prime factor this number6
2 x 3
= 6

20. Prime factor this number8
2 x 4
= 8
2 x 2 x 2 = 8 3
2 = 8

21. Prime factor this number9
3 x 3
= 9 2
3 = 9

22. Prime factor this number10
2 x 5
= 10

23. Prime factor this number12
3 x 4
= 12
3 x 2 x 2 = 12
2 x 2 x 3 = 12 2
2 x 3 = 12

24. Prime factor this number14
2 x 7
= 14

25. Prime factor this number15
3 x 5
= 15

26. Prime factor this number16
4 x 4
= 16
2 x 2 x 2 x 2 = 16 4
2 = 16

27. Prime factor this number18
3 x 6
= 18
3 x 2 x 3 = 18
2 x 3 x 3 = 18
2 x 3 = 18 2

28. Prime factor this number20
4 x 5
= 20
2 x 2 x 5 = 20
2 x 5 = 20 2

29. Prime factor this number21
3 x 7
= 21

30. Prime factor this number22
2 x 11
= 22

31. What about those with variables?
24y2
We do the same as before, we just add the variables with it
2 * 2 * 2 * 3 * y * y
23 * 3 * y2

32. 4-5 Greatest Common Factor
Example
Use prime factorization to find the GCF of 42 and 70.

33. 4-5 Greatest Common Factor
Example
Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.
42 = 7 * = 7 * 10

34. 4-5 Greatest Common Factor
Example
Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.
42 = 7 * = 7 * 10
= 7 * 2 * = 7 * 2 * 5

35. 4-5 Greatest Common Factor
Example
Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.
42 = 7 * = 7 * 10
= 7 * 2 * = 7 * 2 * 5
Then find the common factors.
42 = 7 * 2 * 3
70 = 7 * 2 * 5

36. 4-5 Greatest Common Factor
Example
Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.
42 = 7 * = 7 * 10
= 7 * 2 * = 7 * 2 * 5
Then find the common factors.
42 = 7 * 2 * 3
70 = 7 * 2 * 5

37. 4-5 Greatest Common Factor
Example
Use prime factorization to find the GCF of 42 and 70.
First find the prime factorization of each number.
42 = 7 * = 7 * 10
= 7 * 2 * = 7 * 2 * 5
Then find the common factors.
42 = 7 * 2 * 3
70 = 7 * 2 * 5
The greatest common factor of 42 and 70 is 2 * 7 or 14.

38. 4-5 Greatest Common Factor
Example
Find the greatest common factor of 6m2 and 15m

39. 4-5 Greatest Common Factor
Example
Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number.
6m2 = 6 * m2 15m = 15 * m

40. 4-5 Greatest Common Factor
Example
Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number.
6m2 = 6 * m2 15m = 15 * m
= 3 * 2 * m * m = 3 * 5 * m

41. 4-5 Greatest Common Factor
Example
Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number.
6m2 = 6 * m2 15m = 15 * m
= 3 * 2 * m * m = 3 * 5 * m
Then find the common factors.
6m2 = 3 * 2 * m * m
15m = 3 * 5 * m

42. 4-5 Greatest Common Factor
Example
Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number.
6m2 = 6 * m2 15m = 15 * m
= 3 * 2 * m * m = 3 * 5 * m
Then find the common factors.
6m2 = 3 * 2 * m * m
15m = 3 * 5 * m

43. 4-5 Greatest Common Factor
Example
Find the greatest common factor of 6m2 and 15m
First find the prime factorization of each number.
6m2 = 6 * m2 15m = 15 * m
= 3 * 2 * m * m = 3 * 5 * m
Then find the common factors.
6m2 = 3 * 2 * m * m
15m = 3 * 5 * m
The greatest common factor of 6m2 and 15m is 3 * m or 3m.