# N Divides M Meaning

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.