Solution: The GCF of 136 and 56 is 8
Methods
How to find the GCF of 136 and 56 using Prime Factorization
One way to find the GCF of 136 and 56 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 136?
What are the Factors of 56?
Here is the prime factorization of 136:
2
3
×
1
7
1
2^3 × 17^1
2 3 × 1 7 1
And this is the prime factorization of 56:
2
3
×
7
1
2^3 × 7^1
2 3 × 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 136 and 56 by multiplying all the matching prime factors to get a GCF of 136 and 56 as 4:
Thus, the GCF of 136 and 56 is: 4
How to Find the GCF of 136 and 56 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 136 and 56 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, 136 and 56:
Factors of 136: 1, 2, 4, 8, 17, 34, 68, 136
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 8. Since 8 is the largest of these common factors, the GCF of 136 and 56 would be 8.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 112 and 16?
What is the GCF of 129 and 133?
What is the GCF of 6 and 130?
What is the GCF of 104 and 5?
What is the GCF of 62 and 43?