Solution: The GCF of 23 and 69 is 23
Methods
How to find the GCF of 23 and 69 using Prime Factorization
One way to find the GCF of 23 and 69 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 23?
What are the Factors of 69?
Here is the prime factorization of 23:
2
3
1
23^1
2 3 1
And this is the prime factorization of 69:
3
1
×
2
3
1
3^1 × 23^1
3 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 23 and 69 by multiplying all the matching prime factors to get a GCF of 23 and 69 as 529:
Thus, the GCF of 23 and 69 is: 529
How to Find the GCF of 23 and 69 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 23 and 69 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, 23 and 69:
Factors of 23: 1, 23
Factors of 69: 1, 3, 23, 69
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 23 and 69 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 12 and 146?
What is the GCF of 87 and 47?
What is the GCF of 53 and 40?
What is the GCF of 22 and 29?
What is the GCF of 124 and 118?