Factors are numbers that divide evenly in a number. The greatest common factor of two or more numbers is the largest number that can divide evenly into each of the numbers. Here, you will learn how to find factors and greatest common factors.
You will want to know how to factor numbers when you are trying to simplify fractions.
Factors of the number 12
You can evenly divide 12 by 1, 2, 3, 4, 6 and 12.
Therefore, we can say that 1,2,3,4,6 and 12 are factors of 12.
We can also say that the greatest or largest factor of 12 is 12.
Factors of 12 and 6
You can evenly divide 12 by 1, 2, 3, 4, 6 and 12.
You can evenly divide 6 by 1, 2, 3 and 6.
Now look at both sets of numbers. What is the largest factor of both numbers?
6 is the largest or greatest factor for 12 and 6.
Factors of 8 and 32
You can evenly divide 8 by 1, 2, 4 and 8.
You can evenly divide 32 by 1, 2, 4, 8, 16 and 32.
Therefore the largest common factor of both numbers is 8.
Multiplying Common PRIME Factors
This is another method to find the greatest common factor. Let's take 8 and 32.
The prime factors of 8 are 1 x 2 x 2 x 2.
Notice that the prime factors of 32 are 1 x 2 x 2 x 2 x 2 x 2.
If we multiply the common prime factors of 8 and 32, we get:
1 x 2 x 2 x 2 = 8 which becomes the greatest common factor.
Both methods will help you determine the greatest common factors (GFCs). However, you will need to decide which method you prefer to work with. I have discovered that most of my students prefer the first method. However, if they're not getting it that way, be sure to show them the alternative method.
