N divides M means M divided by N. When `N = 5 `

and `M = 10`

, N divides M is equivalent to `10 ÷ 5`

or 5 divides 10 into 2.

In symbol form, N divides M is denoted as `N|M`

, which is read as N divides M. If N divides M, then N is non-zero because division by zero is invalid.

When a number does not divide another number, the expression is denoted as `N∤M`

, which is read as N does not divide M.

## How to Test if a Number Divides Another Number

We can apply the mathematical definition of divides to determine if N divides M.

Explanation:

N divides M if:

- N, M, and K are integers
- N does not equal zero,
`N ≠ 0`

- and
`M = KN`

Wait a minute, how did K appear out of nowhere???

Well, K will help us determine if N divides M.

Assume that:

`M = 10`

`N = 5`

`K = ?`

If N divides M, then that means `M ÷ N`

(M divided by N).

`M ÷ N = K`

`10 ÷ 5 = 2`

Therefore, `M ÷ N = K`

is the same as `M = KN`

.

So for (`M ÷ N = K`

) to be true, N must be non-zero, and N, M, and K must be integers.

Example:

**Is 3|12 true?**

The question reads as, is 3 divides 12 true?

First, let’s ask: are both N and M integers?

`N = 3`

and `M = 12`

Yes, both N and M are integers.

`M = KN`

(plugin the values)

`12 = K3`

What number times 3 equals 12?

`12 = 4·3`

Is 4 an integer?

Yes, 4 is an integer.

Then, `3|12`

is true.

Lastly, If N divides M, then M is a multiple of N and N is a factor of M.