## Friday, December 13, 2013

### Easiest way to get the greatest common factor of 36 and 48.

Greatest Common Factor 36 and 48

What is the simplest way to find the greatest common factor?

Most teachers say list all factors and then find the largest common one.  There is no need to create a comprehensive list of all factors.  List all factors of the smaller number then go down the list from largest to smallest until you find a common factor.  The first one that you find is the largest common factor.

Let’s illustrate:

Factors of 36 are

2, 3, 4, 6, 9, 12, 18, and 36.

Some hints on the searching process for all factors

36 goes Any number is a factor of itself.

2 goes 36 is even

18 goes 2x18=36.  No number between 18 and 36 will go in evenly.  Think about why!!!

3 goes 3x12=36  No number between 12 and 18 goes into 36 evenly.

4 goes 4x9=36.

10 and 11 don’t go.

5 does not go (36 does not end in either a 5 or 0)

6 goes 6x5=36

7 and 8 do not go.

We are done.

The factors of 36 from greatest to least are 36, 18, 12, 9, 6, 4, 3, and 2.

Now find the largest factor of 36 that goes into 48 evenly.

Naturally, you should start with the largest factor of 36 and work your way down.  REMEMBER YOU ARE LOOKING FOR THE LARGEST COMMON FACTOR.  START WITH THE LARGEST FACTOR OF 36.  ONCE YOU FIND A FACTOR THAT IS COMMON WITH 48 YOU ARE DONE!!!!!

36 does not go into 48 evenly.  Neither does 18 but 12 does.  12 is our answer.  There is no need to look for numbers less than 12 because we are looking for the GREATEST common factor.
36 and 48 are reasonably small numbers so only a little bit of time is wasted by listing all factors of 48.  However, the more difficult you make the problem the more likely it is that you will make a mistake.
Also what would you do with the problem -- find the GCF of 2,362 and 7,400?  Would you start by listing all factors of both numbers?  I HOPE NOT!!!!
Will look at GCF of larger numbers soon.  Will also look at getting GCF through prime factorization soon.
In basketball your coach might say take four passes prior to shooting.  This is very good advice, better than list all factors of both numbers and then find the largest common one.  Still, when your coach says take four passes prior to the shot he or she is not telling you to pass up an open look close to the basket.  At least I hope that is not the advice.