Grasping the Greatest Common Factor

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It feels like just yesterday I was learning about greatest common factors in elementary school. The only difference from learning GCF’s now is that I actually understand it. The greatest common factor is the largest possible number that can divide into a set of numbers equally. An example of this is find the GCF of (24,36), the answer is 12 because 12×2=24 and 12×3=36. There are no larger numbers that divide equally into 24 and 36.

Although the example GCF(24,36) is simple, there is a trick for the more complex problems. For example find the greatest common factor of (2100,3360) seems almost impossible, but I have learned a trick to help speed up the process. Instead of plugging numbers into your calculator you simply need to draw a factor tree for both numbers. The picture provided is what the factor trees should look like.

Once you have the factor trees drawn, you write out the prime numbers for 2100 and 3360. The prime factors of 2400 are 2x2x3x5x5x7, and the prime factors of 3360 are 2x2x2x2x2x3x5x7. The trick to finding the GCF of the 2100 and 3360 is to look at the intersection (overlap) of the numbers. The numbers in read are the overlap (2x2x3x5x7). After you find the intersection, you need to multiply the numbers together (2x2x3x5x7=420). This means that the greatest common factor of 2400 and 3360 is 420. This may look like a lot of work, but it is actually much less work than using your calculator to guess and check numbers.

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