Prime Number Calculator

What's a Prime Number?

Imagine you have a box of crayons. Some boxes can be evenly split between you and your friends, while others can't. If a box of crayons can only be evenly split into one crayon for each person or the whole box for one person, then that's kind of like a prime number!

In number terms, a prime number is a number that can only be divided by 1 and itself without leaving any remainders. It doesn't fit neatly into multiplication groups with other numbers. For example, 2, 3, 5, and 7 are all prime numbers. You can't multiply two different whole numbers to get these prime numbers as a result.

Formula: How do we find a Prime Number?

There isn't a simple formula for generating prime numbers since they're determined by a process of elimination. But, to determine if a number, let's say \( n \), is prime, you'd try to divide it by all whole numbers up to the square root of \( n \). If none of them divides \( n \) evenly, then \( n \) is prime!

Example:

Let's find out if the number 7 is prime:

We'd try to divide 7 by 2, 3 (and any whole number up to the square root of 7). None of these numbers can divide 7 without leaving a remainder. So, 7 is a prime number!

For the number 5: We only need to check if 2 divides it. It doesn't! So, 5 is a prime.

For the number 9: We need to check 2 and 3 (because 3 is the square root of 9). While 2 doesn't divide 9, 3 does (three times!). So, 9 isn't a prime.

What About Breaking Numbers Down Using Primes?

This is called prime factorization. It's like taking a big Lego structure and finding out which prime Lego blocks it's made from.

Method: Trial Division

Remember our earlier example with the number 4? It's like a Lego structure made from two 2-blocks. In the same way, the number 820 is built from the prime blocks 41, 5, and 2 (used twice).

Example:

820 ÷ 2 = 410
410 ÷ 2 = 205
205 ÷ 5 = 41 (since 41 is prime, we stop here)
So, 820 is made up of the prime blocks 2, 2, 5, and 41!

Try it yourself!

Enter any number into our Prime Number Calculator to check if it's prime. And remember, just like crayons, some numbers are meant to stand alone!