Necessary condition

A necessary condition is a concept from logic, reasoning, and mathematics.

It is defined as a conclusion reached as a result of some specific fact. If there is a fact, then necessarily there must also be a fact that is a conclusion. In other words: if a necessary condition is not met, the fact for which that necessary condition is met will definitely not be met.

For example: if any number is divisible by 15, then its last digit is 0 or 5. The fact that a number has a last digit of 0 or 5 is a necessary condition for a number to be divisible by 15.

Therefore, you don't have to check divisibility by means of 15 other numbers (that don't have 0 or 5 as the last digit).

If the last digit of the number were neither 0 nor 5, then it could be deduced that it is not divisible by 15. Thus, the necessary condition for it to be a number divisible by 15 is said to be is that the last digit is 0 or 5.