Solution: The GCF of 145 and 116 is 29
Methods
How to find the GCF of 145 and 116 using Prime Factorization
One way to find the GCF of 145 and 116 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 145?
What are the Factors of 116?
Here is the prime factorization of 145:
5
1
×
2
9
1
5^1 × 29^1
5 1 × 2 9 1
And this is the prime factorization of 116:
2
2
×
2
9
1
2^2 × 29^1
2 2 × 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 145 and 116 by multiplying all the matching prime factors to get a GCF of 145 and 116 as 841:
Thus, the GCF of 145 and 116 is: 841
How to Find the GCF of 145 and 116 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 145 and 116 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, 145 and 116:
Factors of 145: 1, 5, 29, 145
Factors of 116: 1, 2, 4, 29, 58, 116
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 145 and 116 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 144 and 61?
What is the GCF of 2 and 149?
What is the GCF of 50 and 32?
What is the GCF of 114 and 125?
What is the GCF of 60 and 93?