Solution: The GCF of 69 and 23 is 23
Methods
How to find the GCF of 69 and 23 using Prime Factorization
One way to find the GCF of 69 and 23 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 23?
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 23:
2
3
1
23^1
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 23 by multiplying all the matching prime factors to get a GCF of 69 and 23 as 529:
Thus, the GCF of 69 and 23 is: 529
How to Find the GCF of 69 and 23 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 69 and 23 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 23:
Factors of 69: 1, 3, 23, 69
Factors of 23: 1, 23
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 23 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 67 and 107?
What is the GCF of 60 and 44?
What is the GCF of 127 and 25?
What is the GCF of 129 and 50?
What is the GCF of 131 and 39?