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 61.
To see if 61 is prime start at the first factor 2 – as all numbers have 1 as a factor.
Does 2 divide into 61 without leaving a remainder?
No. When dividing 61 by 2 it leaves a remainder of 1.
Increment to the next number: 2 + 1 = 3
Does 3 divide into 61 without leaving a remainder?
No. When dividing 61 by 3 it leaves a remainder of 1.
Increment to the next number: 3 + 1 = 4
Does 4 divide into 61 without leaving a remainder?
No. When dividing 61 by 4 it leaves a remainder of 1.
Increment to the next number: 4 + 1 = 5
Does 5 divide into 61 without leaving a remainder?
No. When dividing 61 by 5 it leaves a remainder of 1.
Increment to the next number: 5 + 1 = 6
Does 6 divide into 61 without leaving a remainder?
No. When dividing 61 by 6 it leaves a remainder of 1.
Increment to the next number: 6 + 1 = 7
Does 7 divide into 61 without leaving a remainder?
No. When dividing 61 by 7 it leaves a remainder of 5.
Increment to the next number: 7 + 1 = 8
As your at, or about to eclipse, the square root of 61 there’s no need to increment any further.
Therefore, as there have been no other factors found, the number 61 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 61 is a prime number.