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**Greatest Common Factor**

GCF Greatest Common Factor

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

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**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

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**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

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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

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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

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**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)

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**… 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

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**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

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**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

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