What is the Greatest Common Factor (GCF) of 30 and 370?
Are you on the hunt for the GCF of 30 and 370? Since you're on this page I'd guess so! In this quick guide, we'll walk you through how to calculate the greatest common factor for any numbers you need to check. Let's jump in!
First off, if you're in a rush, here's the answer to the question "what is the GCF of 30 and 370?":
GCF of 30 and 370 = 10
What is the Greatest Common Factor?
- Greatest Common Denominator (GCD)
- Highest Common Factor (HCF)
- Greatest Common Divisor (GCD)
For most school problems or uses, you can look at the factors of the numbers and find the greatest common factor that way. For 30 and 370 those factors look like this:
- Factors for 30: 1, 2, 3, 5, 6, 10, 15, and 30
- Factors for 370: 1, 2, 5, 10, 37, 74, 185, and 370
As you can see when you list out the factors of each number, 10 is the greatest number that 30 and 370 divides into.
List out all of the prime factors for each number:
- Prime Factors for 30: 2, 3, and 5
- Prime Factors for 370: 2, 5, and 37
Now that we have the list of prime factors, we need to find any which are common for each number.
Looking at the occurences of common prime factors in 30 and 370 we can see that the commonly occuring prime factors are 2 and 5.
To calculate the prime factor, we multiply these numbers together:
GCF = 2 x 5 = 10
Find the GCF Using Euclid's Algorithm
The final method for calculating the GCF of 30 and 370 is to use Euclid's algorithm. This is a more complicated way of calculating the greatest common factor and is really only used by GCD calculators.