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 = 10N = 5K = ?
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.