Solution: The GCF of 56 and 92 is 4
Methods
How to find the GCF of 56 and 92 using Prime Factorization
One way to find the GCF of 56 and 92 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 56?
What are the Factors of 92?
Here is the prime factorization of 56:
2
3
×
7
1
2^3 × 7^1
2 3 × 7 1
And this is the prime factorization of 92:
2
2
×
2
3
1
2^2 × 23^1
2 2 × 2 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 56 and 92 by multiplying all the matching prime factors to get a GCF of 56 and 92 as 4:
Thus, the GCF of 56 and 92 is: 4
How to Find the GCF of 56 and 92 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 56 and 92 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, 56 and 92:
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Factors of 92: 1, 2, 4, 23, 46, 92
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4. Since 4 is the largest of these common factors, the GCF of 56 and 92 would be 4.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 21 and 31?
What is the GCF of 69 and 105?
What is the GCF of 134 and 92?
What is the GCF of 52 and 107?
What is the GCF of 142 and 121?