Solution: The GCF of 36 and 70 is 2
Methods
How to find the GCF of 36 and 70 using Prime Factorization
One way to find the GCF of 36 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 36?
What are the Factors of 70?
Here is the prime factorization of 36:
2
2
×
3
2
2^2 × 3^2
2 2 × 3 2
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 36 and 70 by multiplying all the matching prime factors to get a GCF of 36 and 70 as 4:
Thus, the GCF of 36 and 70 is: 4
How to Find the GCF of 36 and 70 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 36 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, 36 and 70:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
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. Since 2 is the largest of these common factors, the GCF of 36 and 70 would be 2.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 80 and 10?
What is the GCF of 134 and 85?
What is the GCF of 136 and 47?
What is the GCF of 81 and 15?
What is the GCF of 107 and 33?