Solution: The GCF of 28 and 29 is 1
Methods
How to find the GCF of 28 and 29 using Prime Factorization
One way to find the GCF of 28 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 28?
What are the Factors of 29?
Here is the prime factorization of 28:
2
2
×
7
1
2^2 × 7^1
2 2 × 7 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 no matching prime factors. When this is the case, it means that there are no common factors between these two numbers. As a result, the GCF of 28 and 29 is 1.
Thus, the GCF of 28 and 29 is: 1
How to Find the GCF of 28 and 29 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 28 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, 28 and 29:
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 29: 1, 29
When you compare the two lists of factors, you can see that the only common factor is 1. So, in this case, the GCF of 28 and 29 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 54 and 85?
What is the GCF of 126 and 36?
What is the GCF of 76 and 73?
What is the GCF of 71 and 78?
What is the GCF of 3 and 24?