Solution: The GCF of 135 and 54 is 27
Methods
How to find the GCF of 135 and 54 using Prime Factorization
One way to find the GCF of 135 and 54 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 135?
What are the Factors of 54?
Here is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 1
And this is the prime factorization of 54:
2
1
×
3
3
2^1 × 3^3
2 1 × 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 135 and 54 by multiplying all the matching prime factors to get a GCF of 135 and 54 as 9:
Thus, the GCF of 135 and 54 is: 9
How to Find the GCF of 135 and 54 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 135 and 54 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, 135 and 54:
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
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 135 and 54 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 119 and 75?
What is the GCF of 41 and 57?
What is the GCF of 131 and 108?
What is the GCF of 28 and 27?
What is the GCF of 15 and 149?