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

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

Answer 2

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

quotient is zero. Remainder (modulus) is 3.

Answer 3

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.

Answer 4

Conceptually, I think of it this way. By definition, your dividend must be equal to (quotient * divisor) + modulus

Or, solving for modulus: modulus = dividend - (quotient * divisor)

Whenever the dividend is less than the divisor, the quotient is always zero which results in the modulus simply being equal to the dividend.

To illustrate with OP's values:

modulus of 3 and 7 = 3 - (0 * 7) = 3

To illustrate with other values:

1 % 3:
1 - (0 * 3) = 1

2 % 3:
2 - (0 * 3) = 2

Answer 5

• 7 divided by 3 is 2 with a remainder of 1

• 3 divided by 7 is 0 with a remainder of 3

Answer 6

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 7

(7 * 0) + 3 = 3; therefore, the remainder is 3.

Answer 8

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 9

It seems you forgot to mention the surprising case, if the divident is smaller and negative:

-3 % 7 

result: 4