Prime Factorization

Prime Factorization

Used to find the LCM and GCF to help us add and subtract fractions.

Factors• A factor is a number that divides

another number with no remainder.– Examples: factors of 12 are 1 & 12, 2 & 6,

3 & 4

Prime numbers• A number that has only two factors, 1

and itself.– Examples: 2, 3, 5, 7, 11, 13, 17…

Prime Factorization• The prime factorization of a number is

the product of its prime factors.– Example: of 12-

or

€

2 • 2 • 3

€

22 • 3

Factor Trees• Use a factor tree to break down a

number to get to the prime numbers (till you can’t break it down anymore)

orQuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

€

2 • 2 • 5

€

22 • 5

Another example

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

€

2• 2 • 2 • 2

€

24

One more example…

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

€

7• 2 • 2 • 2

€

7• 23

Now you try …• Find the prime factorization of:

– 40

– 48QuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

GCF

The Greatest Common Factor between at least two numbers… used

to simplify fractions.

GCF• The greatest common factor of two or more

numbers is the greatest factor that is in common to those numbers.

• The GCF can be found by:– Listing all the factors of each number and then

finding the largest number in all lists to give the GCF.

– Do a factor tree of each number and the prime factors that are in all trees multiply to give the GCF.

Listing all the factors…• This works best when the numbers are

small and have few factors.

• 12 and 15– Factors of 12: 1, 2, 3, 4, 6, 12– Factors of 15: 1, 3, 5, 15– GCF= 3

Do a factor tree…• This works best when the numbers are large

and have many factors.

These two trees

share a 3 and 5.

Multiply these

two together

and get 15.

GCF=15

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Try another with a factor tree

• 45 and 81

• GCF=3x3=9

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Now you try… Find the GCF• 16 and 24

• 12, 48, 72

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

LCM

Least Common Multiple between at least two numbers… used to find a

common denominator to help add and subtract fractions.

Multiple• The multiple of a number is a product of

that number and a whole number…– Meaning multiply!

• Multiples of 5:– 5, 10, 15, 20, 25, 30…

• Multiples of 3:– 3, 6, 9, 12, 15, 18, 21…

LCM• Least Common Multiple is the smallest

multiple of two or more numbers.• The easiest way to find the LCM:

– Start to list all the multiples of the numbers involved and stop as soon as you have a number in common to both lists.

– Ex: between 3 and 5• 5, 10, 15, 20…• 3, 6, 9, 12, 15…• So the LCM is 15!

You try it!• Find the LCM between 4 and 9

– Make a list of multiples of each number.– 4, 8, 12, 16, 20, 24, 28, 32, 36, 40– 9, 18, 27, 36..– LCM = 36!