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    Greatest Common Factors

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    تاريخ التسجيل : 16/02/2011

    Greatest Common Factors

    مُساهمة  Admin في الأربعاء فبراير 16, 2011 12:11 pm



    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.
    ________________________________________
    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:

    ________________________________________
    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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