A common factor is a whole number that is a factor of two or more

nonzero whole numbers.

The Greatest Common Factor (GCF) can be found two ways.

1. Listing factors of two numbers and finding the largest one they have in common.

2. Prime factorization

1,2,3,4,5,6,10,12,15,20,30,60

List the factors of 96:1,2,3,4,6,8,12,16,24,32,48,96

find the common factors

List the factors of 60:

List the factors of 60:

1,2,3,4,5,6,10,12,15,20,30,60

List the factors of 96

1,2,3,4,6,8,12,16,24,32,48,96

Find the largest factor: 12

Prime and Prime and CompositeComposite Prime - A natural number which has exactly

two distinct natural number divisors: 1 and itself.

3 5 1x 3 1x5

Composite - A natural number which can be divided evenly by numbers other than 1 or itself.

6 8 1x6 1x8 2x3 2x4

Prime and Prime and CompositeComposite Tricks of the TradeTricks of the Trade

Prime numbers are always an odd number except for 2

All even numbers can be divided by 2.

Any number ending in a 5 can be divided by 5.

Any number ending in a 0 can be divided by 5 or 10.

When dealing with multiples of 9, the sum of the answer equals 9. (Only up to 10)

Ex. 9x2 = 18 (1+8=9) 9x6= 54 (5+4=9)

9x9 = 81 (8+1=9) 9x10=90 (9+0=9)

60

2 30

2 15

3 5

96

2 48

2 24

2 12

2 6

2 32 x 2 x 3 = 12

… or do prime factorization. Circle all the primes the 2 numbers have in common and multiply one set of them to get your GCF.

Find the GCF of 48 and 24:

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Finding GCF by Making a ListFinding GCF by Making a List

48 24

12 4 12 2

3 4 2 2 6 2

2 2 3 2

48=3 x 2 x 2 x 2 x 2 24=3 x 2 x 2 x 2

GCF= 3 x 23 = 3 x 8 = 24, so 24 is the GCF

Find GCF Through Prime FactorizationFind GCF Through Prime Factorization