Solution: The GCF of 105 and 63 is 21
Methods
How to find the GCF of 105 and 63 using Prime Factorization
One way to find the GCF of 105 and 63 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 105?
What are the Factors of 63?
Here is the prime factorization of 105:
3
1
×
5
1
×
7
1
3^1 × 5^1 × 7^1
3 1 × 5 1 × 7 1
And this is the prime factorization of 63:
3
2
×
7
1
3^2 × 7^1
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 105 and 63 by multiplying all the matching prime factors to get a GCF of 105 and 63 as 441:
Thus, the GCF of 105 and 63 is: 441
How to Find the GCF of 105 and 63 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 63 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, 105 and 63:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 63: 1, 3, 7, 9, 21, 63
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 105 and 63 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 30 and 22?
What is the GCF of 129 and 43?
What is the GCF of 55 and 79?
What is the GCF of 120 and 104?
What is the GCF of 75 and 34?