How can you tell if a number is prime? And what is the fastest way to tell if a number is a prime number?

A prime number is a number that has just two factors: the number 1 and itself. Therefore, when finding all the factors of a number if you end up with just two numbers then you have a prime number.

Using the same process as you would normally when finding factors for a given number, the same is applied when determining whether a number is prime. Once you’ve completed finding all the factors simply add up all the factors and if you see just the number 1 and your original number, then you likely have a prime number.

## Step By Step Prime Number Example

Here is the process if you want to find if a number is a prime number. I’ll use for this example the number 47.

To see if 47 is prime start at the first factor 2 – as all numbers have 1 as a factor.

Does 2 divide into 47 without leaving a remainder?

No. When dividing 47 by 2 it leaves a remainder of 1.

Increment to the next number: 2 + 1 = 3

Does 3 divide into 47 without leaving a remainder?

No. When dividing 47 by 3 it leaves a remainder of 2.

Increment to the next number: 3 + 1 = 4

Does 4 divide into 47 without leaving a remainder?

No. When dividing 47 by 4 it leaves a remainder of 3.

Increment to the next number: 4 + 1 = 5

Does 5 divide into 47 without leaving a remainder?

No. When dividing 47 by 5 it leaves a remainder of 2.

Increment to the next number: 5 + 1 = 6

Does 6 divide into 47 without leaving a remainder?

No. When dividing 47 by 6 it leaves a remainder of 5.

Increment to the next number: 6 + 1 = 7

As your at, or about to eclipse, the square root of 47 there’s no need to increment any further.

Therefore, as there have been no other factors found, the number 47
**
is
**
a prime number.

As you can see from the step by step guide it’s exactly the same process when finding factors of a number, however, you can short-circuit the process by stopping whenever you find a factor that isn’t 1 or the original number itself.

## Summary

A prime number is a number that has only 2 factors: the number 1 and itself.

The number 47 is
**
not
**
a prime number.