Solution: The GCF of 45 and 27 is 9
Methods
How to find the GCF of 45 and 27 using Prime Factorization
One way to find the GCF of 45 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 45?
What are the Factors of 27?
Here is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 5 1
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 45 and 27 by multiplying all the matching prime factors to get a GCF of 45 and 27 as 9:
Thus, the GCF of 45 and 27 is: 9
How to Find the GCF of 45 and 27 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 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, 45 and 27:
Factors of 45: 1, 3, 5, 9, 15, 45
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. Since 9 is the largest of these common factors, the GCF of 45 and 27 would be 9.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 89 and 41?
What is the GCF of 147 and 37?
What is the GCF of 57 and 27?
What is the GCF of 133 and 74?
What is the GCF of 128 and 108?