Solution: The GCF of 30 and 70 is 10
Methods
How to find the GCF of 30 and 70 using Prime Factorization
One way to find the GCF of 30 and 70 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 30?
What are the Factors of 70?
Here is the prime factorization of 30:
2
1
×
3
1
×
5
1
2^1 × 3^1 × 5^1
2 1 × 3 1 × 5 1
And this is the prime factorization of 70:
2
1
×
5
1
×
7
1
2^1 × 5^1 × 7^1
2 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 30 and 70 by multiplying all the matching prime factors to get a GCF of 30 and 70 as 100:
Thus, the GCF of 30 and 70 is: 100
How to Find the GCF of 30 and 70 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 30 and 70 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, 30 and 70:
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
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 30 and 70 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 122 and 80?
What is the GCF of 124 and 138?
What is the GCF of 38 and 141?
What is the GCF of 69 and 79?
What is the GCF of 43 and 92?