Greatest Common Factors
The Greatest Common Factor (G.C.F.) of two numbers is the largest number that is a divisor of both. It is sometimes called the Greatest Common Divisor. It can be used to simplify (or reduce) fractions. Don't let the "greatest" in the name fool you - the GCF is no larger than the smallest of the numbers.
HINTS:
GREATEST is biggest or largest.
COMMON is something shared or in common.
FACTORS are the parts of multiplication facts.
EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 6 and 10.
6 = 2 * 3 You can divide 6 by 2 or by 3
6 = 1 * 6 You can divide 6 by 1 or by 6
Therefore 1, 2, 3, and 6 are all factors of six.
10 = 2 * 5 You can divide 10 by 2 or by 5
10 = 1 * 10 You can divide 10 by 1 or by 10
Therefore 1, 2, 5, and 10 are all factors of ten.
Both 6 and 10 can be divided by 1 and by 2; 2 is greater than 1, so 2 is the Greatest Common Factor (G.C.F.) of 6 and 10.
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You can also use the prime factorization method to find the Greatest Common Factor:
EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 36 and 54.
36 = 2 * 2 * 3 * 3
54 = 2 * 3 * 3 * 3
Both have 2 * 3 * 3 in common:
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Usually you can find the Greatest Common Factor fairly easily by experimenting with possible divisors:
Start with the smaller number; it is the largest divisor of itself.
Is it a divisor of the larger number? If so, you have the G.C.F.; if not:
What is the next-largest divisor of the smaller number; is IT a divisor of the other number?
Continue until you find a number that will divide into BOTH. Sometimes only the number '1' will work as a common divisor; for example: 21 and 16 have no common factor other than 1.
EXAMPLE:
Find the Greatest Common Factor (G.C.F.) of 10 and 30.
Will 10 go into 30? Yes:
G.C.F. = 10
Find the Greatest Common Factor (G.C.F.) of 24 and 18.
Will 18 go into 24? No.
Next pair: 2 * 9 = 18
Will 9 go into 24? No.
Next pair: 3 * 6 = 18
Will 6 go into 24? Yes:
G.C.F. = 6
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