Solution: The GCF of 13 and 10 is 1
Methods
How to find the GCF of 13 and 10 using Prime Factorization
One way to find the GCF of 13 and 10 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 13?
What are the Factors of 10?
Here is the prime factorization of 13:
1
3
1
13^1
1 3 1
And this is the prime factorization of 10:
2
1
×
5
1
2^1 × 5^1
2 1 × 5 1
When you compare the prime factorization of these two numbers, you can see that there are no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 13 and 10 is 1.
Thus, the GCF of 13 and 10 is: 1
How to Find the GCF of 13 and 10 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 13 and 10 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, 13 and 10:
Factors of 13: 1, 13
Factors of 10: 1, 2, 5, 10
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 13 and 10 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 112 and 97?
What is the GCF of 100 and 126?
What is the GCF of 27 and 71?
What is the GCF of 134 and 1?
What is the GCF of 133 and 90?