Solution: The GCF of 36 and 11 is 1
Methods
How to find the GCF of 36 and 11 using Prime Factorization
One way to find the GCF of 36 and 11 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 36?
What are the Factors of 11?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
And this is the prime factorization of 11:
1
1
1
11^1
1 1 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 36 and 11 is 1.
Thus, the GCF of 36 and 11 is: 1
How to Find the GCF of 36 and 11 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 and 11 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, 36 and 11:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 11: 1, 11
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 36 and 11 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 48 and 61?
What is the GCF of 135 and 29?
What is the GCF of 45 and 58?
What is the GCF of 82 and 144?
What is the GCF of 72 and 69?