Solution: The GCF of 140 and 126 is 14
Methods
How to find the GCF of 140 and 126 using Prime Factorization
One way to find the GCF of 140 and 126 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 126?
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 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 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 140 and 126 by multiplying all the matching prime factors to get a GCF of 140 and 126 as 196:
Thus, the GCF of 140 and 126 is: 196
How to Find the GCF of 140 and 126 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 140 and 126 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 126:
Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
When you compare the two lists of factors, you can see that the common factor(s) are 1, 2, 7, 14. Since 14 is the largest of these common factors, the GCF of 140 and 126 would be 14.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 115 and 68?
What is the GCF of 47 and 84?
What is the GCF of 61 and 20?
What is the GCF of 49 and 139?
What is the GCF of 97 and 89?