Solution: The GCF of 70 and 100 is 10
Methods
How to find the GCF of 70 and 100 using Prime Factorization
One way to find the GCF of 70 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 70?
What are the Factors of 100?
Here is the prime factorization of 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 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 70 and 100 by multiplying all the matching prime factors to get a GCF of 70 and 100 as 100:
Thus, the GCF of 70 and 100 is: 100
How to Find the GCF of 70 and 100 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 70 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, 70 and 100:
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
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, 2, 5, 10. Since 10 is the largest of these common factors, the GCF of 70 and 100 would be 10.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 5 and 101?
What is the GCF of 135 and 46?
What is the GCF of 18 and 85?
What is the GCF of 89 and 75?
What is the GCF of 150 and 122?