Solution: The GCF of 45 and 102 is 3
Methods
How to find the GCF of 45 and 102 using Prime Factorization
One way to find the GCF of 45 and 102 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 102?
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 102:
2
1
×
3
1
×
1
7
1
2^1 × 3^1 × 17^1
2 1 × 3 1 × 1 7 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 45 and 102 by multiplying all the matching prime factors to get a GCF of 45 and 102 as 9:
Thus, the GCF of 45 and 102 is: 9
How to Find the GCF of 45 and 102 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 45 and 102 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 102:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3. Since 3 is the largest of these common factors, the GCF of 45 and 102 would be 3.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 130 and 145?
What is the GCF of 142 and 99?
What is the GCF of 61 and 110?
What is the GCF of 12 and 66?
What is the GCF of 55 and 150?