# Factors of a Number

How to find the factors of a number: 2 examples their solutions.

## Example 1

### Solution

To find the factors of 30,
write down the pairs of natural numbers
whose product is 30.

Start from 1 and 30.
1⋅30 = 30
So 1 and 30 are the factors of 30.

Increase the first number.
2⋅15 = 30
So 2 and 15 are the factors of 30.

3⋅10 = 30
So 3 and 10 are the factors of 30.

4⋅7.5 = 30
But 7.5 is not a natural number.
So 4 and 7.5 are not the factors of 30.

5⋅6 = 30
So 5 and 6 are the factors of 30.

6⋅5 = 30
But you already found the factors 5 and 6.
So stop finding the factors.

Just like this case,
if the first number gets greater than the second number,
stop finding the factors.

So the factors of 30 are
1, 2, 3, 5, 6, 10, 15, and 30.

## Example 2

### Solution

To find the factors of 16,
write down the pairs of natural numbers
whose product is 16.

Start from 1 and 16.
1⋅16 = 16
So 1 and 16 are the factors of 16.

Increase the first number.
2⋅8 = 16
So 2 and 8 are the factors of 16.

3⋅(16/3) = 16
But 16/3 is not a natural number.
So 3 and 16/3 are not the factors of 16.

4⋅4 = 16
So 4 is the factor of 16.

If the first number gets greater than 4,
it'll be greater than the second number.
So stop finding the factors.

So the factors of 16 are
1, 2, 4, 8, and 16.

## Prime Number

### Definition

A prime number is a number
that has two factors: 1 and itself.
2, 3, 5, 7, 11, 13, 17, ... are prime numbers.

1 has only one factor: 1.
So 1 is not a prime.