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.


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.


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.