FRACTURE

Prime Number: A prime number is a positive integer greater than $1$ that has exactly two factors—$1$ and itself.

Composite Number: A composite number is a positive integer greater than $1$ that has more than two factors, including $1$ and the number itself.

In simple terms, a composite number can be divided evenly by natural numbers. Since prime numbers are natural numbers, some of those divisors may also be prime numbers. However, a prime number cannot be divided evenly by any natural number except $1$ and itself.

Let’s take the composite number $60$ as an example:

$$ \begin{aligned} 60 &= 1 \times 60 \\ &= 2 \times 30 \\ &= 3 \times 20 \\ &= 4 \times 15\\ &= 5 \times 12\\ &= 6 \times 10 \end{aligned} $$

This means that $60$ can be divided evenly by these $12$ numbers:

$$ 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 $$

But if $60$ were a prime number, the only numbers that could divide it evenly would be $1$ and $60$ itself.

From this simple idea, we discover something fascinating—something universal about numbers.

If a number can be written as a product of two numbers, and those numbers can be further broken down into products of smaller numbers, we can continue this process until we reach a point where every number in the product can no longer be broken down any further.

At that point, we reach the building blocks of numbers: prime numbers.

This process is called Prime Factorization.

$$ \begin{aligned} 60 &= 2 \times 30 \\ &= 2 \times 2 \times 15 \\ &= 2 \times 2 \times 3 \times 5 \\ &= 2^2 \times 3 \times 5 \longrightarrow \text{All primes} \end{aligned} $$

Prime numbers are like the atoms of whole numbers. They cannot be broken down into smaller factors, but when combined together, they create the incredibly vast and infinite world of numbers.

How cool!