Solution: The GCF of 105 and 45 is 15
Methods
How to find the GCF of 105 and 45 using Prime Factorization
One way to find the GCF of 105 and 45 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 105?
What are the Factors of 45?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
And this is the prime factorization of 45:
3
2
×
5
1
3^2 × 5^1
3 2 × 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 105 and 45 by multiplying all the matching prime factors to get a GCF of 105 and 45 as 225:
Thus, the GCF of 105 and 45 is: 225
How to Find the GCF of 105 and 45 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 45 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, 105 and 45:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 45: 1, 3, 5, 9, 15, 45
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 5, 15. Since 15 is the largest of these common factors, the GCF of 105 and 45 would be 15.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 62 and 32?
What is the GCF of 122 and 46?
What is the GCF of 109 and 8?
What is the GCF of 102 and 137?
What is the GCF of 134 and 2?