What is the GCF (greatest comon factor) of 84 and 114?

Question

I cant find it. Please help!

Answer 1

First you have to break each number into its primary multiples.

84 is even, so divide it by 2.
84 / 2 = 42

42 is even, so divide it by 2 also.
42 / 2 = 21

21 can be divided by 3.
21 / 3 = 7

So the multiples of 84 are: 2 * 2 * 3 * 7.

Now, let's find the multiples of 114.
Since 114 is even, divide it by 2.
114 / 2 = 57

57 can be divided by 3.
57 / 3 = 19.

Nineteen is a prime number, so we can't go any further.
The multiples of 114 are:
2 * 3 * 19

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2 * 2 * 3 * 7 = 84
2 * 3 * 19 = 114

Correction: The greatest common factor of 84 and 114 equals:
2 * 3 = 6

A very clear example of what I tried to explain is at:
http://www.math.com/school/subject1/lessons/S1U3L2GL.html

Good luck - hope this helps.
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(Thanks to Smiley Girl for pointing out my error).

Answer 2

I'm not sure what it is either but I'll help you get started.
84 and 114 are both divisible by 2, so divide and you get
42 and 57 are both divisible by 3, so divide and you get...

Keep doing this division until you can't divide both numbers by the same factor. When you are stopped, multiply together all of the numbers that you divided by, and that will be your GCF. So far you will be multiplying at least 2 and 3.

Hope this helps. Good Luck.

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Watch that you don't find the LCM like Mitch did below. The GCF will be smaller than the two numbers you are given originally.

Answer 3

do your homework?