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Greatest Common Factor
Common factor and Greatest Common Factor
• Common factor: A whole number that is a factor of two or more nonzero whole numbers.
largest number of the • Greatest common factor, (GCF): the common factors of two or more nonzero whole numbers.
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Greatest Common Factor
Prime factorization can be used to find the GCF of two or more numbers.
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Greatest Common Factor
• Finding the greatest common factor of two or more numbers using prime factorization
• Write the prime factorization of each number
• Identify the common prime factors
• Multiply the common prime factors
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Greatest Common Factor
Find the greatest common factor of 24, 36, and 240
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Greatest Common Factor
Find the greatest common factor of 24, 36, and 240
Step 1) Write the prime factorization of each number
3
24 = 2 2 2 3 = 2 32
2
36 = 2 2 3 3 = 2 3
4
240 = 2 2 2 2 3 5 = 2 3 5
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Greatest Common Factor
Find the greatest common factor of 24, 36, and 240
Step 1) Write the prime factorization of each number
3
24 = 2 2 2 3 = 2 32
2
36 = 2 2 3 3 = 2 3
4
240 = 2 2 2 2 3 5 = 2 3 5
Step 2) Identify the common prime factors
Common factors are 2, 2, and 3
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Greatest Common Factor
Find the greatest common factor of 24, 36, and 240
Step 1) Write the prime factorization of each number
3
24 = 2 2 2 3 = 2 32
2
36 = 2 2 3 3 = 2 3
4
240 = 2 2 2 2 3 5 = 2 3 5
Step 2) Identify the common prime factors
Common factors are 2, 2, and 3
Step 3) Multiply the common prime factors 2 2 3 = 12
so 12 is the greatest common factor of 24, 36, and 240
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Greatest Common Factor
Find the greatest common factor of 42 and 70
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Greatest Common Factor
Find the greatest common factor of 42 and 70
42 = 2 3 7
70 = 2 5 7
common prime factors are 2 and 7
greatest common factor = 2 7 = 14
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Greatest Common Factor
Find the greatest common factor of 16, 40, and 88
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Greatest Common Factor
Find the greatest common factor of 16, 40, and 88
4
16 = 2 2 2 2 = 2
3
40 = 2 2 2 5 = 2 5
3
88 = 2 2 2 11 = 2 11
common prime factors are 2,2, and 2
greatest common factor is 2 2 2 = 8
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Greatest Common Factor
Find the greatest common factor of 45 and 112
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Greatest Common Factor
Find the greatest common factor of 45 and 112
2
45 = 3 3 5 = 3 5
4
112 = 2 2 2 2 7 = 2 7
There are no common prime factors
What would the greatest common factor be in this case?
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Greatest Common Factor
Relatively Prime
relatively prime if • Two or more numbers are said to be their greatest common factor is 1.
**** Note *****
This does not mean the numbers themselves are prime
It means they do not share any common prime factors.
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