1. Greatest Common Factor
GCF
Greatest Common Factor

2. A common factor is a whole number that is a factor of two or more nonzero whole numbers.

3. 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

4. find the common factors
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 common factors

5. 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

6. Prime and Composite
Prime - A natural number which has exactly two distinct natural number divisors: 1 and itself.
1x x5
Composite - A natural number which can be divided evenly by numbers other than 1 or itself.
1x x8
2x x4

7. Prime and Composite Tricks 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) x6= 54 (5+4=9)
9x9 = 81 (8+1=9) x10=90 (9+0=9)

8. … or do prime factorization
… or do prime factorization. Circle all the primes the 2 numbers have in common and multiply one set of them to get your GCF. 96 60 48 2 2 30 24 2 15 2 12 2 3 5 6 2
2 x 2 x 3 = 12
GCF 2 3

9. Greatest Common Factor
Finding GCF by Making a List
Find the GCF of 48 and 24:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Greatest Common Factor

10. Find GCF Through Prime Factorization
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