Why is the rest (remainder) of both operations 5%3 and 5%-3 different?

Question

I understand that being the negative divisor, the rest will be negative, but should it be -2 and not -1

a = 5%3
b = 5%-3
print (a, b)

#output a=2 and b=-1

Answer 1

Andrew nailed it! 👍

I find it helpful to remember that modulo operation always return the LARGEST possible remainder between 0 and the divisor. Otherwise, the number we get can go on infinitely to both ends.

For example,
...
❎ 5 = -1 × 3 + 8
❎ 5 = 0 × 3 + 5
✅ 5 = 1 × 3 + 2
❎ 5 = 2 × 3 + (-1)
❎ 5 = 3 × 3 + (-4)
...

and for negative divisor,
...
❎ 5 = -4 × (-3) + (-7)
❎ 5 = -3 × (-3) + (-4)
✅ 5 = -2 × (-3) + (-1)
❎ 5 = -1 × (-3) + 2
❎ 5 = 0 × (-3) + 5
...

Hopefully it helps! 😉

Answer 2

dividend = divisor * quotient + remainder

For a, quotient is 1, and: 5 = 3 * 1 + 2
For b, quotient is -2, and: 5 = -3 * (-2) + (-1)