Solution: The GCF of 116 and 145 is 29
Methods
How to find the GCF of 116 and 145 using Prime Factorization
One way to find the GCF of 116 and 145 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 116?
What are the Factors of 145?
Here is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 2 9 1
And this is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 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 116 and 145 by multiplying all the matching prime factors to get a GCF of 116 and 145 as 841:
Thus, the GCF of 116 and 145 is: 841
How to Find the GCF of 116 and 145 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 116 and 145 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, 116 and 145:
Factors of 116: 1, 2, 4, 29, 58, 116
Factors of 145: 1, 5, 29, 145
When you compare the two lists of factors, you can see that the common factor(s) are 1, 29. Since 29 is the largest of these common factors, the GCF of 116 and 145 would be 29.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 89 and 112?
What is the GCF of 136 and 117?
What is the GCF of 61 and 146?
What is the GCF of 149 and 100?
What is the GCF of 148 and 107?