Solution: The GCF of 74 and 106 is 2
Methods
How to find the GCF of 74 and 106 using Prime Factorization
One way to find the GCF of 74 and 106 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 106?
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 106:
2
1
×
5
3
1
2^1 × 53^1
2 1 × 5 3 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 74 and 106 by multiplying all the matching prime factors to get a GCF of 74 and 106 as 4:
Thus, the GCF of 74 and 106 is: 4
How to Find the GCF of 74 and 106 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 74 and 106 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 106:
Factors of 74: 1, 2, 37, 74
Factors of 106: 1, 2, 53, 106
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2. Since 2 is the largest of these common factors, the GCF of 74 and 106 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 19 and 35?
What is the GCF of 29 and 128?
What is the GCF of 107 and 21?
What is the GCF of 51 and 95?
What is the GCF of 102 and 31?