Finding Factors of a Natural Number

Finding Factors of a Natural Number

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

Example 1

Find the factors of 30.

Think of a pair of natural numbers
whose product is 30.

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

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

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

5⋅6 = 30.
So 5 and 6 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.

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

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

Example 2

Find the factors of 16.

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

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

4⋅4 = 16.
So 4 is the factor of 16.

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

Example 3

Find the factors of 7.

1⋅7 = 7.
So 1 and 7 are the factors of 7.

Just like 7,
numbers that have only 2 factors, 1 and itself,
are called prime numbers:
2, 3, 5, 7, 11, 13, ... .

Example 4

Find the factors of 1.

1⋅1 = 1.
So 1, itself, is the factor of 1.

In other words,
1 has only 1 factor: itself.