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Posted on 2007-07-24

Please provide procedure for finding Greatest Common Factor(GCM) of whole numbers. For example, what is the GCM of 27 and 72.

8 Comments

The second website above is too advance for my needs. I am asking a Fifth Grade Math question.

Example for 27 and 72 :

27 = 3 * 3 * 3

72 = 2 * 2 * 2 * 3 * 3

The common divisors for 27 and 72 are thus 3 and 3 (twice), so the GCD is 3 * 3 = 9

Here's a more beginner friendly page :

http://en.wikipedia.org/wi

The algorithms that ozo posted are more advanced, and are preferrable for bigger numbers. The technique I illustrated is only feasible for small numbers.

1) List # = f1 * f2 * ... * fn (for each number)

2) simplify down to simpliest factors

72 ----- 2 * 36

|------- 2 * 18

|----------2 * 9

|-------3 * 3

3) You arrive at Infinity08's approach above (2*2*2*3*3)

4) Do same for other number(s)

5) Multiply highest factor that is common to both lists (in this case 3*3 = 9)

6) For your level (5th grade)... test:

---> 27 / 9 = 3

---> 72 / 9 = 8

There are some other ways involving number layouts... I'll leave this to your teacher to show (as it often took 2 or 3 days for students to grasp when explained in class.

I'd hate to confuse you over the site.

Second rule: The GCD of any two nonzero numbers x and y is the same as (assuming x >= y) the GCD of (x modulo y) and y. GCD(x,y) = GCD(x modulo y, y)

So, to solve GCD(27,72):

The second rule says that GCD(27,72) = GCD(72 modulo 27, 27)

72 modulo 27 = 18, so

GCD(27,72) = GCD(18,27)

Using the second rule again, GCD(18,27) = GCD(27 modulo 18, 18)

27 modulo 18 = 9

GCD(27,72) = GCD(18,27) = GCD (9,18) = GCD(18 modulo 9 ,9)

18 modulo 9 = 0

GCD(27,72) = GCD(18,27) = GCD (9,18) = GCD(0,9)

By the first rule, GCD(0,9) is 9. Therefore GCD(27,72) = 9

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