Solution: The GCF of 45 and 120 is 15
Methods
How to find the GCF of 45 and 120 using Prime Factorization
One way to find the GCF of 45 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 45?
What are the Factors of 120?
Here is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 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 45 and 120 by multiplying all the matching prime factors to get a GCF of 45 and 120 as 225:
Thus, the GCF of 45 and 120 is: 225
How to Find the GCF of 45 and 120 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 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, 45 and 120:
Factors of 45: 1, 3, 5, 9, 15, 45
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, 3, 5, 15. Since 15 is the largest of these common factors, the GCF of 45 and 120 would be 15.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 8 and 76?
What is the GCF of 111 and 98?
What is the GCF of 83 and 74?
What is the GCF of 92 and 122?
What is the GCF of 68 and 36?