Solution: The GCF of 145 and 29 is 29
Methods
How to find the GCF of 145 and 29 using Prime Factorization
One way to find the GCF of 145 and 29 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 29?
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 29:
2
9
1
29^1
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 145 and 29 by multiplying all the matching prime factors to get a GCF of 145 and 29 as 841:
Thus, the GCF of 145 and 29 is: 841
How to Find the GCF of 145 and 29 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 145 and 29 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 29:
Factors of 145: 1, 5, 29, 145
Factors of 29: 1, 29
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 29 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 29 and 101?
What is the GCF of 82 and 5?
What is the GCF of 113 and 24?
What is the GCF of 121 and 6?
What is the GCF of 49 and 94?