Greatest Common Factors
Hello. This math post is on greatest common factors (GCFs) between two or more numbers.
Topics
- Review Of Number Factors
- Finding Greatest Common Factors
- Practice Problems
- Solutions To Practice Problems
Review Of Number Factors
Given a number such as 24, number factors can be obtained by determining numbers that multiply together to obtain 24.
Some ways to multiply whole numbers to get 24 are:
- 1 x 24
- 2 x 12
- 3 x 8
- 4 x 6
- 6 x 4
- 8 x 3
- 12 x 2
- 24 x 1
When it comes to listing number factors, there is no need to list duplicates. Just list the unique numbers that appear.
The number factors for 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Finding Greatest Common Factors
Be able to find greatest common factors does not have real world applications but it is a nice tool to have in the algebra toolbox. Greatest common factors are helpful when it comes to reducing fractions to lowest terms and for high school factoring in algebra.
It is best to show how to find greatest common factors with examples.
Example One
Find the GCF of 10 and 2.
The factors for 2 are 1 and 2.
For the number 10, the factors are 1, 2, 5 and 10. (I like to start from 1 and work all the way to 10 for finding factors.)
What are the common factors between 2 and 10? These are 1 and 2.
From the common factors of 1 and 2, the greatest common factor would be 2.
Example Two
Determine the GCF for 42 and 28.
Factors for 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
For the number 28, the factors are 1, 2, 4, 7, 14 and 28.
Common factors for 42 and 28 are 1, 2, 7 and 14.
The greatest common factor here would be 14.
Example Three - Three Numbers
A natural extension is working with more than two numbers. Here is an example with three numbers.
What is the GCF for the numbers 9, 12 and 33?
The strategy is not much different here. There is more to keep track of.
Factors of 9: 1, 3, 9
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 33: 1, 3, 11, 33
The common factors for 9, 12 and 33 are: 1 and 3.
This would make the GCF 3.
Practice Problems
Here are some practice problems to help with understanding and to improve speed.
Determine the GCF for the following sets of numbers.
5 and 20
9 and 24
26 and 65
11 and 110
16 and 40
5, 10 and 55
24, 72 and 60
Solutions To Practice Problems
GCF of 5 and 20 is 5.
GCF of 9 and 24 is 3.
GCF of 26 and 65 is 13.
GCF of 11 and 110 is 11.
GCF of 16 and 40 is 8.
GCF of 5, 10 and 55 is 5.
GCF of 24, 72 and 60 is 12.
