Solution: The GCF of 74 and 17 is 1
Methods
How to find the GCF of 74 and 17 using Prime Factorization
One way to find the GCF of 74 and 17 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 74?
What are the Factors of 17?
Here is the prime factorization of 74:
2
1
×
3
7
1
2^1 × 37^1
2 1 × 3 7 1
And this is the prime factorization of 17:
1
7
1
17^1
1 7 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 74 and 17 is 1.
Thus, the GCF of 74 and 17 is: 1
How to Find the GCF of 74 and 17 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 74 and 17 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, 74 and 17:
Factors of 74: 1, 2, 37, 74
Factors of 17: 1, 17
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 74 and 17 is 1.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 105 and 124?
What is the GCF of 81 and 143?
What is the GCF of 56 and 101?
What is the GCF of 83 and 93?
What is the GCF of 130 and 133?