Solution: The GCF of 126 and 49 is 7
Methods
How to find the GCF of 126 and 49 using Prime Factorization
One way to find the GCF of 126 and 49 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 126?
What are the Factors of 49?
Here is the prime factorization of 126:
2
1
×
3
2
×
7
1
2^1 × 3^2 × 7^1
2 1 × 3 2 × 7 1
And this is the prime factorization of 49:
7
2
7^2
7 2
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 126 and 49 by multiplying all the matching prime factors to get a GCF of 126 and 49 as 49:
Thus, the GCF of 126 and 49 is: 49
How to Find the GCF of 126 and 49 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 49 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, 126 and 49:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 49: 1, 7, 49
When you compare the two lists of factors, you can see that the common factor(s) are 1, 7. Since 7 is the largest of these common factors, the GCF of 126 and 49 would be 7.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 42 and 73?
What is the GCF of 89 and 106?
What is the GCF of 53 and 116?
What is the GCF of 65 and 80?
What is the GCF of 38 and 10?