Solution: The GCF of 90 and 135 is 45
Methods
How to find the GCF of 90 and 135 using Prime Factorization
One way to find the GCF of 90 and 135 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 90?
What are the Factors of 135?
Here is the prime factorization of 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 2 × 5 1
And this is the prime factorization of 135:
3
3
×
5
1
3^3 × 5^1
3 3 × 5 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 90 and 135 by multiplying all the matching prime factors to get a GCF of 90 and 135 as 225:
Thus, the GCF of 90 and 135 is: 225
How to Find the GCF of 90 and 135 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 90 and 135 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, 90 and 135:
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 135: 1, 3, 5, 9, 15, 27, 45, 135
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 5, 9, 15, 45. Since 45 is the largest of these common factors, the GCF of 90 and 135 would be 45.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 128 and 78?
What is the GCF of 136 and 22?
What is the GCF of 64 and 63?
What is the GCF of 4 and 61?
What is the GCF of 28 and 17?