Solution: The GCF of 10 and 84 is 2
Methods
How to find the GCF of 10 and 84 using Prime Factorization
One way to find the GCF of 10 and 84 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 10?
What are the Factors of 84?
Here is the prime factorization of 10:
2
1
×
5
1
2^1 × 5^1
2 1 × 5 1
And this is the prime factorization of 84:
2
2
×
3
1
×
7
1
2^2 × 3^1 × 7^1
2 2 × 3 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 10 and 84 by multiplying all the matching prime factors to get a GCF of 10 and 84 as 4:
Thus, the GCF of 10 and 84 is: 4
How to Find the GCF of 10 and 84 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 10 and 84 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, 10 and 84:
Factors of 10: 1, 2, 5, 10
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
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 10 and 84 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 89 and 95?
What is the GCF of 49 and 81?
What is the GCF of 13 and 149?
What is the GCF of 139 and 57?
What is the GCF of 35 and 44?