Solution: The GCF of 65 and 120 is 5
Methods
How to find the GCF of 65 and 120 using Prime Factorization
One way to find the GCF of 65 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 65?
What are the Factors of 120?
Here is the prime factorization of 65:
5
1
×
1
3
1
5^1 × 13^1
5 1 × 1 3 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 65 and 120 by multiplying all the matching prime factors to get a GCF of 65 and 120 as 25:
Thus, the GCF of 65 and 120 is: 25
How to Find the GCF of 65 and 120 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 65 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, 65 and 120:
Factors of 65: 1, 5, 13, 65
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, 5. Since 5 is the largest of these common factors, the GCF of 65 and 120 would be 5.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 146 and 114?
What is the GCF of 128 and 149?
What is the GCF of 23 and 24?
What is the GCF of 21 and 73?
What is the GCF of 122 and 148?