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 49.
To see if 49 is prime start at the first factor 2 – as all numbers have 1 as a factor.
Does 2 divide into 49 without leaving a remainder?
No. When dividing 49 by 2 it leaves a remainder of 1.
Increment to the next number: 2 + 1 = 3
Does 3 divide into 49 without leaving a remainder?
No. When dividing 49 by 3 it leaves a remainder of 1.
Increment to the next number: 3 + 1 = 4
Does 4 divide into 49 without leaving a remainder?
No. When dividing 49 by 4 it leaves a remainder of 1.
Increment to the next number: 4 + 1 = 5
Does 5 divide into 49 without leaving a remainder?
No. When dividing 49 by 5 it leaves a remainder of 4.
Increment to the next number: 5 + 1 = 6
Does 6 divide into 49 without leaving a remainder?
No. When dividing 49 by 6 it leaves a remainder of 1.
Increment to the next number: 6 + 1 = 7
Does 7 divide into 49 without leaving a remainder?
Yes! The number 49 when divided by 7 is 7 without a remainder.
Therefore, as 49 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 49 is a prime number.