Solution: The GCF of 69 and 115 is 23
Methods
How to find the GCF of 69 and 115 using Prime Factorization
One way to find the GCF of 69 and 115 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 69?
What are the Factors of 115?
Here is the prime factorization of 69:
3
1
×
2
3
1
3^1 × 23^1
3 1 × 2 3 1
And this is the prime factorization of 115:
5
1
×
2
3
1
5^1 × 23^1
5 1 × 2 3 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 69 and 115 by multiplying all the matching prime factors to get a GCF of 69 and 115 as 529:
Thus, the GCF of 69 and 115 is: 529
How to Find the GCF of 69 and 115 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 69 and 115 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, 69 and 115:
Factors of 69: 1, 3, 23, 69
Factors of 115: 1, 5, 23, 115
When you compare the two lists of factors, you can see that the common factor(s) are 1, 23. Since 23 is the largest of these common factors, the GCF of 69 and 115 would be 23.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 23 and 28?
What is the GCF of 20 and 143?
What is the GCF of 84 and 118?
What is the GCF of 83 and 129?
What is the GCF of 141 and 103?