Solution: The GCF of 68 and 140 is 4
Methods
How to find the GCF of 68 and 140 using Prime Factorization
One way to find the GCF of 68 and 140 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 68?
What are the Factors of 140?
Here is the prime factorization of 68:
2
2
×
1
7
1
2^2 × 17^1
2 2 × 1 7 1
And this is the prime factorization of 140:
2
2
×
5
1
×
7
1
2^2 × 5^1 × 7^1
2 2 × 5 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 68 and 140 by multiplying all the matching prime factors to get a GCF of 68 and 140 as 4:
Thus, the GCF of 68 and 140 is: 4
How to Find the GCF of 68 and 140 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 68 and 140 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, 68 and 140:
Factors of 68: 1, 2, 4, 17, 34, 68
Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
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 68 and 140 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 42 and 7?
What is the GCF of 95 and 135?
What is the GCF of 134 and 32?
What is the GCF of 83 and 109?
What is the GCF of 105 and 22?