Prime numbers are numbers that have exactly 2 factors: 1 and itself.
Composite numbersare numbers that have 3 or more factors.
The only natural number that is neither Prime nor Composite is 1. The number 1 is often referred to as the multiplicative identity or the empty product.
Watch this video to learn more about prime numbers!
The Sieve of Eratosthenes
The Sieve of Eratosthenes is a smart and simple way to find all the prime numbers up to a certain number (like 100).
🪜 How the Sieve Works (Step by Step)
Step 1: 1 is NOT a prime number, so we grey it out.
Step 2: Highlight the smallest number left (i.e. 2). 2 is the first prime number. Colour it Green.
Step 3: Cross out multiples of 2. All numbers that can be divided by 2 (except 2 itself) are not prime. So we cross out: 4, 6, 8, 10, 12…
Step 4: Repeat Steps 2 and Step 3. The next smallest number left will be a prime then cross out all its multiples.
You stop when your prime number (E.g. 11) is bigger than the square root of 100 (which is 10). After that, any number not crossed out must be prime.
Why do you think 1 is not a prime number?
A simple reason is that if 1 was a prime number then using the Sieve to remove all multiples of 1, the game would be over before it even began.