Solution: The GCF of 126 and 105 is 21
Methods
How to find the GCF of 126 and 105 using Prime Factorization
One way to find the GCF of 126 and 105 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 105?
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 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 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 126 and 105 by multiplying all the matching prime factors to get a GCF of 126 and 105 as 441:
Thus, the GCF of 126 and 105 is: 441
How to Find the GCF of 126 and 105 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 126 and 105 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 105:
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
When you compare the two lists of factors, you can see that the common factor(s) are 1, 3, 7, 21. Since 21 is the largest of these common factors, the GCF of 126 and 105 would be 21.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 114 and 27?
What is the GCF of 87 and 121?
What is the GCF of 34 and 35?
What is the GCF of 69 and 146?
What is the GCF of 4 and 22?