Solution: The GCF of 40 and 120 is 40
Methods
How to find the GCF of 40 and 120 using Prime Factorization
One way to find the GCF of 40 and 120 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 40?
What are the Factors of 120?
Here is the prime factorization of 40:
2
3
×
5
1
2^3 × 5^1
2 3 × 5 1
And this is the prime factorization of 120:
2
3
×
3
1
×
5
1
2^3 × 3^1 × 5^1
2 3 × 3 1 × 5 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 40 and 120 by multiplying all the matching prime factors to get a GCF of 40 and 120 as 100:
Thus, the GCF of 40 and 120 is: 100
How to Find the GCF of 40 and 120 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 40 and 120 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 40 and 120:
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 5, 8, 10, 20, 40. Since 40 is the largest of these common factors, the GCF of 40 and 120 would be 40.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 17 and 139?
What is the GCF of 101 and 127?
What is the GCF of 48 and 63?
What is the GCF of 1 and 121?
What is the GCF of 129 and 29?