Solution: The GCF of 29 and 145 is 29
Methods
How to find the GCF of 29 and 145 using Prime Factorization
One way to find the GCF of 29 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 29?
What are the Factors of 145?
Here is the prime factorization of 29:
2
9
1
29^1
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 29 and 145 by multiplying all the matching prime factors to get a GCF of 29 and 145 as 841:
Thus, the GCF of 29 and 145 is: 841
How to Find the GCF of 29 and 145 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 29 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, 29 and 145:
Factors of 29: 1, 29
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 29 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 86 and 54?
What is the GCF of 67 and 96?
What is the GCF of 120 and 16?
What is the GCF of 74 and 99?
What is the GCF of 148 and 28?