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Factors, Prime Numbers & Composite Numbers
Definition
• Product – An answer to a multiplication problem.
7 x 8 = 56
Product
Definition
• Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors
Definition
• Factor – a number that divides evenly into another number.
56 ÷ 8 = 7
Factors
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 7Product: 42
Factors: 7 and 9Product: 63
Factors: 5 and 8Product: 40
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.
Examples of Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…
2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Here’s How You Do It
Take out numbers that have a composite factor of 2
2 3 5 7 9
11 13 15 17 19
21 23 25 27 29
31 33 35 37 39
41 43 45 47 49
51 53 55 57 59
61 63 65 67 69
71 73 75 77 79
81 83 85 87 89
91 93 95 97 99
Here’s How You Do It
Take out numbers that have a composite factor of 2
2 3 5 7 9
11 13 15 17 19
21 23 25 27 29
31 33 35 37 39
41 43 45 47 49
51 53 55 57 59
61 63 65 67 69
71 73 75 77 79
81 83 85 87 89
91 93 95 97 99
Here’s How You Do It
Take out numbers that have a composite factor of 3
2 3 5 7
11 13 17 19
23 25 29
31 35 37
41 43 47 49
53 55 59
61 65 67
71 73 77 79
83 85 89
91 95 97
Here’s How You Do It
Take out numbers that have a composite factor of 3
2 3 5 7
11 13 17 19
23 25 29
31 35 37
41 43 47 49
53 55 59
61 65 67
71 73 77 79
83 85 89
91 95 97
Here’s How You Do It
Take out numbers that have a composite factor of 5
2 3 5 7
11 13 17 19
23 29
31 37
41 43 47 49
53 59
61 67
71 73 77 79
83 89
91 97
Here’s How You Do It
Take out numbers that have a composite factor of 5
2 3 5 7
11 13 17 19
23 29
31 37
41 43 47 49
53 59
61 67
71 73 77 79
83 89
91 97
Here’s How You Do It
Take out numbers that have a composite factor of 7
2 3 5 7
11 13 17 19
23 29
31 37
41 43 47
53 59
61 67
71 73 79
83 89
97
The PRIME Numbers!
Take out numbers that have a composite factor of 7
Example: The number 8. The factors of 8 are 1, 2, 4, 8.
Definition
• Composite number – a number that has more than two factors.
Examples of Composite Numbers
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, …
One is special because . . .
One is not prime.(because it doesnot have exactly
two differentfactors).
One is not Composite.(because it doesnot have morethan 2 factors).
Definition
• Prime Factorization – A way to write a composite number as the product of its prime factors.
2 x 2 x 3 = 12or
22 x 3 = 12
How to do a Prime Factorization
48Step 1 – Write down any composite number.
- - Factor Tree Method - -
Step 2 – Start dividing bythe 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
How to do a Prime Factorization
48Step 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
How to do a Prime Factorization
48Step 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
How to do a Prime Factorization
48Step 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
24 x 3 = 48
Find the Prime Factorization
4
2 x 2
22 = 4
Prime Factorization
Prime Factorization in Exponential Form
Find the Prime Factorization
6
2 x 3 = 6Prime Factorization
Find the Prime Factorization
273 x 9
33 = 273 x 3 x 3Prime Factorization
Prime Factorization in Exponential Form
Find the Prime Factorization
122 x 6
22 x 3 = 122 x 2 x 3Prime Factorization
Prime Factorization in Exponential Form
Find the Prime Factorization
182 x 9
2 x 32 = 182 x 3 x 3 Prime Factorization
Prime Factorization in Exponential Form
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.
How to do a Prime Factorization
18Step 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
How to do a Prime Factorization
18Step 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 nextrung 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
#
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 32
Step 6 – Write the Prime Factorization in Exponential Form.
56
- - Ladder Method - -
2
7
Prime Factorization 2 x 2 x 2 x 7
Prime Factorization in Exponential Form 23
x 7
282
142 Prime
#
Find the Prime Factorization
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.
The End
