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101740_6FactorsandPrimeandCompositeNumbers.pdf

Factors, Prime Numbers &

Composite Numbers

by Carol Edelstein

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 = 422) 63 ÷9 = 73) 8 x 5 = 40Factors: 6 and 7Product: 42

Factors: 7 and 9

Product: 63

Factors: 5 and 8

Product: 40

Example: 7 is primebecause 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 Numbers2, 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 Numbers4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, ...

One is special because . . .

One is not prime.

(because it doesnot have exactlytwo 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= 12

22x 3 = 12

How to do a Prime Factorization

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

How to do a Prime Factorization

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 242 x 2 x 12

How to do a Prime Factorization

Step 5 -Check the factors.

If they are prime, proceed to Step 6.

If they are not, repeat Step 4.

- - Factor Tree Method - -

2 x24

2 x 2 x122 x2 x2 x6

How to do a Prime Factorization

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 x242 x 2 x122 x2 x2 x62 x2 x2 x2 x3

22224 4 4 4 xxxx3333= 48

Find the Prime Factorization

44442 x 2

2 2= 4

Prime Factorization

in Exponential Form

Find the Prime Factorization

62 x 3====6

Prime Factorization

Find the Prime Factorization

273 x 9

3 3= 27

3 x 3 x 3

Prime Factorization

in Exponential Form

Find the Prime Factorization

122 x 6

22x 3 = 12

2 x 2 x 3

Prime FactorizationPrime Factorization

in Exponential Form

Find the Prime Factorization

182 x 9

2 x 3

2= 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

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

How to do a Prime Factorization

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 #

How to do a Prime Factorization

18- - Ladder Method - -

2 93
3

Prime

Factorization

2x 3x 3

Prime Factorization

in Exponential Form 2x 32

Step 6 -Write the

Prime Factorization in

Exponential Form.

56- - Ladder Method - -

2 7

Prime

Factorization

2x 2x 2 x 7

Prime Factorization

in Exponential Form

23 x 728

2 142
Prime #

Find the Prime Factorization

Summary

• One is not a prime orcomposite 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

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