Greatest Common Factors, Least Common MultiplesDate: 8/29/96 at 20:35:44 From: Anonymous Subject: Greatest Common Factors, Explained! Please explain greatest common factors, how to find them, and how they are different from lowest common multiples. Thank you, Amber Date: 8/30/96 at 13:41:11 From: Doctor Tom Subject: Re: Greatest Common Factors, Explained! Hi Amber, The "greatest common factor" is also often called the "greatest common divisor", or GCD, and it is the largest number that divides all of the numbers in question. For example, the GCD of 12 and 18 is 6, since 6 divides both numbers evenly and nothing larger does. A couple of other examples: the GCD of 7 and 17 is 1 the GCD of 7 and 49 is 7 the GCD of 100 and 72 is 4 Here's a method to find the GCD of two numbers, which I will show by example. Apply exactly the same method in your case. I'll find the GCD of 12070 and 41820: 41820 = 3*12070 + 5610 12070 = 2*5610 + 850 5610 = 6*850 + 510 850 = 1*510 + 340 510 = 1*340 + 170 340 = 2*170 + 0 As soon as the remainder is 0, you've got the answer: 170. These are big numbers; usually the number of steps to the GCD is much smaller. If you need to find the GCD of three numbers, A, B, and C, for example, let D = GCD(A, B) and your answer will be the GCD of D and C, and so on. The least common multiple is the smallest number that all your numbers divide, which is sort of the opposite of the GCD. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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