Lesson: Greatest Common Divisor (GCD)

Comment on Greatest Common Divisor (GCD)

What if there are two numbers with two 2's & two 3's....etc
Do you multiply 2 X 2 X 3 X 3?
greenlight-admin's picture

Yes, exactly. For example, let's find the GCD of 72 and 108
72 = 2 x 2 x 2 x 3 x 3
108 = 2 x 2 x 3 x 3 x 3
So, the GCD = 2 x 2 x 3 x 3 = 36

I was doing some of the Kahn problems on GCF, and I came up with a way I like for doing GCF problems, in addition to the methods already shown.

Basically, as I'm sure you know (and maybe you mentioned in a video), people find common factors (not gcf) all the time when reducing fractions. So, I noticed if you just wrote down the common factor for each step, you could multiply all of them at the end and you would have your GCF.

For example, one problem had 18 chocolate bars and 12 cookies, and wanted the greatest number of identical groups, or bags that could be created. We could solve like so:

18/12 --> cf 2 --> 9/6 --> cf 3 --> 3/2 gcf = 2x3 = 6

So, we have 6 groups, each of 3 bars and 2 cookies. Or 6 groups of 5 each (composed of parts of 3 and 2). It also helps to draw a rectangle that's 6 by 5 with the understanding that the 5 side can be broken down into 2 and 3.

I think this is a nice additional way to think of how to find GCF. At least I like it.

greenlight-admin's picture

Hey Kevin,

That's a great strategy, and it works for any two integers.
The ONLY drawback is that it doesn't work for more that 2 numbers.


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