Solution: The GCF of 81 and 27 is 27
Methods
How to find the GCF of 81 and 27 using Prime Factorization
One way to find the GCF of 81 and 27 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 81?
What are the Factors of 27?
Here is the prime factorization of 81:
3
4
3^4
3 4
And this is the prime factorization of 27:
3
3
3^3
3 3
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 81 and 27 by multiplying all the matching prime factors to get a GCF of 81 and 27 as 9:
Thus, the GCF of 81 and 27 is: 9
How to Find the GCF of 81 and 27 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 81 and 27 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, 81 and 27:
Factors of 81: 1, 3, 9, 27, 81
Factors of 27: 1, 3, 9, 27
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 9, 27. Since 27 is the largest of these common factors, the GCF of 81 and 27 would be 27.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 115 and 129?
What is the GCF of 96 and 88?
What is the GCF of 74 and 86?
What is the GCF of 41 and 92?
What is the GCF of 57 and 130?