How does modulus of a smaller dividend and larger divisor work?

Question

7 % 3 = 1 (remainder 1)

how does
3 % 7 (remainder ?)

work?

Answer 1

As long as they're both positive, the remainder will be equal to the dividend. If one or both is negative, then you get reminded that % is really the remainder operator, not the modulus operator. A modulus will always be positive, but a remainder can be negative.

Answer 2

The most simple and effective catch to remember would be: Whenever dividend is less than the divisor, modulus is just that dividend.

Let's formulate this:

if x < y, then x % y = x 

Answer 3

7 goes into 3? zero times with 3 left over.

quotient is zero. Remainder (modulus) is 3.

Answer 4

a % q = r means there is a x so that q * x + r = a.

So, 7 % 3 = 1 because 3 * 2 + 1 = 7,

and 3 % 7 = 3 because 7 * 0 + 3 = 3

Answer 5

remainder of 3/7 is 3..since it went 0 times with 3 remainder so 3%7 = 3

Answer 6

The same way. The quotient is 0 (3 / 7 with fractional part discarded). The remainder then satisfies:

(a / b) * b + (a % b) = a
(3 / 7) * 7 + (3 % 7) = 3
0 * 7 + (3 % 7) = 3
(3 % 7) = 3

This is defined in C99 §6.5.5, Multiplicative operators.