Factors, Prime Numbers and Composite numbers

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 7
Product: 42
Factors: 7 and 9
Product: 63
Factors: 5 and 8
Product: 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…

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

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
x 3 = 12

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

48
Step 3 – Check the factors.
If they are prime, you are done.
If they are not, proceed to Step 4.
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

48
If they are prime, proceed to Step 6.
If they are not, repeat Step 4.
2 x 24
2 x 2 x 12
2 x 2 x 2 x 6

48
If they are not, repeat Step 4.
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

6
2 x 3 =6
Prime Factorization

27
3 x 9
33
= 27
3 x 3 x 3
Prime Factorization
Prime Factorization
in Exponential Form

12
2 x 6
22
x 3 = 12
2 x 2 x 3
Prime Factorization
Prime Factorization
in Exponential Form

18
2 x 9
2 x 32
= 18
2 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.

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

18
If not, continue the process.
Step 4 – Continue dividing the # on the next
rung of the ladder by the prime #s (start with 2).
2
9
3
3
Step 5 – Repeat this process until the # on
the next rung of the ladder is prime.
Prime
#

18
2
9
3
3
Prime
Factorization 2x
3x
3
Prime Factorization
in Exponential Form 2x
32
Step 6 – Write the
Prime Factorization in
Exponential Form.

56
2
7
Prime
Factorization 2x
2x
2 x
7
Prime Factorization
in Exponential Form 23 x
7
28
2
14
2
Prime
#

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.

Factors, Prime Numbers and Composite numbers

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