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 27.
To see if 27 is prime start at the first factor 2 – as all numbers have 1 as a factor.
Does 2 divide into 27 without leaving a remainder?
No. When dividing 27 by 2 it leaves a remainder of 1.
Increment to the next number: 2 + 1 = 3
Does 3 divide into 27 without leaving a remainder?
Yes! The number 27 when divided by 3 is 9 without a remainder.
Therefore, as 27 has more than 2 factors this number is not 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 27 is not a prime number as it has the factors of 1, 3, 9 and 27 as factors.