 # GREATEST COMMON FACTOR

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GREATEST COMMON FACTOR

GREATEST COMMON FACTOR GCF
The largest factor two or more numbers have in common. To find the GCF of two or more numbers, you can make a list of all the factors or use prime factorization.

Make a list List all of the factors of each number.
Identify the common factors. The greatest of the common factors is the GCF.

24 = 32 = Make a list 32 24 The common factors are: 1, 2, 4, 8
1, 2, 3, 4,6, 8, 12, 24 1, 2, 4, 8, 16, 32 32 1 x 32 2 x 16 4 x 8 24 1 x 24 2 x 12 3 x 8 4 x 6 The common factors are: 1, 2, 4, 8 The GCF = 8

Use Prime Factorization
Write the prime factorization of each number. Identify all of the common prime factors. The product of the common prime factors is the GCF.

Use Prime Factorization
24 = 32 = 2 2 2 3 24 ^ 6 x 4 ^ ^ 2 x 3 2 x 2 24=2 x 2 x 2 x 3

Use Prime Factorization
24 = 32 = 2 2 2 3 2 2 2 2 2 32 ^ 4 x 8 ^ ^ 2 x 2 2 x 4 ^ 2 x 2 32=2 x 2 x 2 x 2 x 2

Use Prime Factorization
24 = 32 = 2 2 2 3 2 2 2 2 2 2 2 2 x x 4 2 x The GCF = 8

Use Prime Factorization
15 = 45 = 3 5 3 5 3 3 5 x 15 = 3 x 5 15 45 = 3 x 3 x 5 The GCF = 15

Use Prime Factorization
6= 44 = 2 3 2 2 11 2 6 = 2 x 3 44 = 2 x 2 x 11 The GCF = 2

Use Prime Factorization
25 = 56 = 5 5 2 2 2 7 25 = 5 x 5 56 = 2 x 2 x 2 x 7 The GCF = 1

Use Prime Factorization
25 = 56 = 5 5 2 2 2 7 If there are no common prime factors the GCF is one. The GCF = 1

Use Prime Factorization
11 = 22 = 11 11 2 11 11 = prime number 22 = 2 x 11 The GCF = 11

Use Prime Factorization
12 = 18 = 60 = 2 2 3 2 3 3 5 2 2 3 2 3 12 = 2 x 2 x 3 x 18 = 2 x 3 x 3 60 = 2 x 2 x 3 x 5 The GCF = 6