Greatest Common Factor GCF Greatest Common Factor

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

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

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 Composite 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 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) 9x6= 54 (5+4=9) 9x9 = 81 (8+1=9) 9x10=90 (9+0=9)

… 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

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

Find GCF Through Prime Factorization 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