Understanding modulus

Question

I don't really understand how modulus division works. I was calculating 5 % 6 and wound up with 5 and I don't understand why. I understand modulus without decimal values. E. G 16%3 = 5 r 1.

What don't you understand about it? Do you know what the modulus operator means? 6 goes into 5 exactly 0 times, with a remainder of 5. — David, Aug 31 '15 at 17:48
By the way: a question about mathematics is not on topic here and should be asked on the [Stack Exchange for maths](http://math.stackexchange.com/). — bcsb1001, Aug 31 '15 at 17:51
I'm voting to close this question as off-topic because this is not a programming question, and you can find an explanation of this very quickly and easily by searching the web. — Jesper, Aug 31 '15 at 18:19
Modulus (MOD) Operator Repeated Sequences: https://www.bennadel.com/blog/2240-creating-repeated-sequences-with-the-modulus-mod-operator.htm — Tyler Rafferty, Feb 10 '17 at 22:08

score 1 · Answer 1 · answered Aug 31 '15 at 17:42

1

The problem with your calculation 5 % 6 is that it will ALWAYS give you remainder 5. If you tried 6 % 5, that will give you 1 for an answer.

answered Aug 31 '15 at 17:42

ryekayo

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bcsb1001 · Answer 2 · 2015-08-31T17:55:50.280

This isn't a programming question, as modulus is a mathematical operator not at all unique to Java or any programming language, but 5 mod 6 = 5 as it is the remainder after dividing by 6 (5 < 6 so the remainder is 5). 6 mod 5 = 1, as 6 > 5, so you subtract 5, then you are left with 1 and 1 < 6.

If it helps, here is a pseudocode illustration of modulus (for positive integers):

integer mod(integer a, integer b) {
    if a < b:
        return a
    else:
        return mod(a - b, b)
}

score 0 · Answer 3 · answered Aug 31 '15 at 17:45

num1 % num2

The modulus operator divides num1 by num2 as integers (in other words, all results of division are rounded down to the nearest whole number) and outputs the remainder. In your case, 5/6 = 0 with a remainder of 5.

Another way of expressing the remainder is: num1 = x*num2 + R

Where x is the result of the integer division num1/num2 and R is the remainder, which is the output of the modules operator. Again in your case, 5 = 0*6 + 5.

score 0 · Answer 4 · answered Aug 31 '15 at 18:34

Modulus operator is similar to the "remainder", but there are a technicalities that make it different when negative numbers are involved.

However, for your example, think of 5 % 6 as "the remainder of 5 divided by 6" Read left to right, just like division.

Understanding modulus

4 Answers4