greatest common factor. greatest common factor gcf the largest factor two or more numbers have in...
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GREATEST COMMON FACTOR
GREATEST COMMON FACTORGCF
• 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.
Make a list
24 =
32 = 24
1 x 24
2 x 12
3 x 8
4 x 6
32
1 x 32
2 x 16
4 x 8
1, 2, 3, 4,6, 8, 12, 24
1, 2, 4, 8, 16, 32
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 = 24
^6 x 4
^2 x 3
^2 x 2
24=2 x 2 x 2 x 3
2 2 2 3
Use Prime Factorization
24 =
32 =32 ^
4 x 8 ^
2 x 2 ^
2 x 4
32=2 x 2 x 2 x 2 x 2
^ 2 x 2
2 2 2 32 2 2 2 2
Use Prime Factorization
24 =
32 =
2 2 2 32 2 2 2 2
2 2 2x x
4 x 2
8The GCF =
Use Prime Factorization
15 =
45 =
3 53 5 3
3 5x
15The GCF =
15 15 = 3 x 5
45 = 3 x 3 x 5
Use Prime Factorization
6=
44 =
2 32 2 11
2
2The GCF =
6 = 2 x 3
44 = 2 x 2 x 11
Use Prime Factorization
25 =
56 =
5 5
2 2 2
1The GCF =
7
25 = 5 x 5
56 = 2 x 2 x 2 x 7
Use Prime Factorization
25 =
56 =
5 5
2 2 2
1The GCF =
7
If there are no common prime factors the GCF is one.
Use Prime Factorization
11 =
22 =
1111 2
11
11The GCF =
11 = prime number
22 = 2 x 11
32
Use Prime Factorization12 =
18 =
60 =
2 2 32 3
2 3x
6The GCF =
32 5
12 = 2 x 2 x 3
18 = 2 x 3 x 3
60 = 2 x 2 x 3 x 5