Prime Number Calculator

What is a Prime Number?

A prime number is like a special building block in math. It's a whole number greater than 1 that can only be divided evenly by 1 and itself. Think of it as a number that stands alone and can't be split into equal groups!

How to Identify Prime Numbers

To find out if a number is prime, we try dividing it by smaller numbers. If it can be divided evenly (with no remainder) by any number other than 1 and itself, it's not prime. If it can only be divided evenly by 1 and itself, it's prime!

Mathematical Definition

We can write the definition of a prime number like this:

\[ p \text{ is prime if } p > 1 \text{ and if } p = ab \text{ then } a = 1 \text{ or } b = 1 \]

This means:

• \(p\) is the number we're checking
• \(p\) must be greater than 1
• If we can write \(p\) as a product \(ab\), then either \(a\) or \(b\) must be 1

Steps to Check if a Number is Prime

1. Make sure the number is greater than 1
2. Start with 2 as a divisor
3. Divide the number by the divisor
4. If there's no remainder, it's not prime
5. If there is a remainder, increase the divisor by 1
6. Repeat steps 3-5 until the divisor is greater than the square root of the number
7. If no divisors were found, the number is prime!

Example and Visual Representation

Let's check if 7 is a prime number:

We'll try dividing 7 by numbers from 2 to \(\sqrt{7}\) (about 2.6):

7 ÷ 2 = 3 remainder 1

No other numbers to check!

So, 7 is a prime number!

Let's show this with a picture:

In this picture, we see the number 7 inside a circle. The green line shows that it can't be divided evenly by any number except 1 and itself. That's what makes it prime!