Solution: The GCF of 76 and 42 is 2
Methods
How to find the GCF of 76 and 42 using Prime Factorization
One way to find the GCF of 76 and 42 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 76?
What are the Factors of 42?
Here is the prime factorization of 76:
2
2
×
1
9
1
2^2 × 19^1
2 2 × 1 9 1
And this is the prime factorization of 42:
2
1
×
3
1
×
7
1
2^1 × 3^1 × 7^1
2 1 × 3 1 × 7 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 76 and 42 by multiplying all the matching prime factors to get a GCF of 76 and 42 as 4:
Thus, the GCF of 76 and 42 is: 4
How to Find the GCF of 76 and 42 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 76 and 42 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, 76 and 42:
Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
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 76 and 42 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 98 and 59?
What is the GCF of 127 and 73?
What is the GCF of 55 and 142?
What is the GCF of 132 and 13?
What is the GCF of 133 and 75?