Solution: The GCF of 90 and 58 is 2
Methods
How to find the GCF of 90 and 58 using Prime Factorization
One way to find the GCF of 90 and 58 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 90?
What are the Factors of 58?
Here is the prime factorization of 90:
2
1
×
3
2
×
5
1
2^1 × 3^2 × 5^1
2 1 × 3 2 × 5 1
And this is the prime factorization of 58:
2
1
×
2
9
1
2^1 × 29^1
2 1 × 2 9 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 90 and 58 by multiplying all the matching prime factors to get a GCF of 90 and 58 as 4:
Thus, the GCF of 90 and 58 is: 4
How to Find the GCF of 90 and 58 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 90 and 58 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, 90 and 58:
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 58: 1, 2, 29, 58
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 90 and 58 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 109 and 110?
What is the GCF of 18 and 11?
What is the GCF of 15 and 119?
What is the GCF of 88 and 144?
What is the GCF of 80 and 51?