Solution: The GCF of 140 and 80 is 20
Methods
How to find the GCF of 140 and 80 using Prime Factorization
One way to find the GCF of 140 and 80 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 140?
What are the Factors of 80?
Here is the prime factorization of 140:
2
2
×
5
1
×
7
1
2^2 × 5^1 × 7^1
2 2 × 5 1 × 7 1
And this is the prime factorization of 80:
2
4
×
5
1
2^4 × 5^1
2 4 × 5 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 140 and 80 by multiplying all the matching prime factors to get a GCF of 140 and 80 as 100:
Thus, the GCF of 140 and 80 is: 100
How to Find the GCF of 140 and 80 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 140 and 80 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, 140 and 80:
Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 4, 5, 10, 20. Since 20 is the largest of these common factors, the GCF of 140 and 80 would be 20.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 35 and 100?
What is the GCF of 90 and 69?
What is the GCF of 66 and 113?
What is the GCF of 101 and 125?
What is the GCF of 83 and 30?