Solution: The GCF of 35 and 10 is 5
Methods
How to find the GCF of 35 and 10 using Prime Factorization
One way to find the GCF of 35 and 10 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 35?
What are the Factors of 10?
Here is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 1 × 7 1
And this is the prime factorization of 10:
2
1
×
5
1
2^1 × 5^1
2 1 × 5 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 35 and 10 by multiplying all the matching prime factors to get a GCF of 35 and 10 as 25:
Thus, the GCF of 35 and 10 is: 25
How to Find the GCF of 35 and 10 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 35 and 10 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, 35 and 10:
Factors of 35: 1, 5, 7, 35
Factors of 10: 1, 2, 5, 10
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 35 and 10 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 105 and 131?
What is the GCF of 97 and 36?
What is the GCF of 21 and 42?
What is the GCF of 19 and 92?
What is the GCF of 134 and 137?