Solution: The GCF of 105 and 100 is 5
Methods
How to find the GCF of 105 and 100 using Prime Factorization
One way to find the GCF of 105 and 100 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 100?
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 100:
2
2
×
5
2
2^2 × 5^2
2 2 × 5 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 105 and 100 by multiplying all the matching prime factors to get a GCF of 105 and 100 as 25:
Thus, the GCF of 105 and 100 is: 25
How to Find the GCF of 105 and 100 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 105 and 100 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 100:
Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 105 and 100 would be 5.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 80 and 36?
What is the GCF of 19 and 130?
What is the GCF of 108 and 61?
What is the GCF of 97 and 134?
What is the GCF of 124 and 138?