Please explain why 17 @ = 17

Question

I am new to Java, actually programming in general. I understand that the modulus operator (%) returns the remainder of two numbers, however, I do not understand why 17 % 40 = 1

Answer 1

Maybe this is a different and more helpful way to think about it.

When we apply division to integer numbers a and b, we are really trying to relate a and b like this:

a = Q * b + R

a is some multiple of b, plus some leftover. Q and R are integers; to keep this simple, let's also just think of non-negative numbers. The multiple, Q, is the quotient and leftover, R, is the remainder -- the smallest ones that make this relation work.

In most languages, a / b gives you Q, and and a % b gives you R. (In fact processors tend to compute both at once -- these are so related.)

So if a is 17 and b is 40, it only works if you write:

17 = 0 * 40 + 17

This is why a % b must be 17.

(Note that it gets more complex when considering negative numbers.)