How Does Modulus Divison Work

Question

I don\'t really understand how modulus division works. I was calculating 27 % 16 and wound up with 11 and I don\'t understand why.

I can\'t

Answer 1

The simple formula for calculating modulus is :-

[Dividend-{(Dividend/Divisor)*Divisor}]

So, 27 % 16 :-

27- {(27/16)*16}

27-{1*16}

Answer= 11

Note:

All calculations are with integers. In case of a decimal quotient, the part after the decimal is to be ignored/truncated.

eg: 27/16= 1.6875 is to be taken as just 1 in the above mentioned formula. 0.6875 is ignored.

Compilers of computer languages treat an integer with decimal part the same way (by truncating after the decimal) as well

Answer 2

The result of a modulo division is the remainder of an integer division of the given numbers.

That means:

27 / 16 = 1, remainder 11
=> 27 mod 16 = 11

Other examples:

30 / 3 = 10, remainder 0
=> 30 mod 3 = 0

35 / 3 = 11, remainder 2
=> 35 mod 3 = 2

Answer 3

Write out a table starting with 0.

{0,1,2,3,4}

Continue the table in rows.

{0,1,2,3,4}
{5,6,7,8,9}
{10,11,12,13,14}

Everything in column one is a multiple of 5. Everything in column 2 is a multiple of 5 with 1 as a remainder. Now the abstract part: You can write that (1) as 1/5 or as a decimal expansion. The modulus operator returns only the column, or in another way of thinking, it returns the remainder on long division. You are dealing in modulo(5). Different modulus, different table. Think of a Hash Table.

Answer 4

Maybe the example with an clock could help you understand the modulo.

A familiar use of modular arithmetic is its use in the 12-hour clock, in which the day is divided into two 12 hour periods.

Lets say we have currently this time: 15:00
But you could also say it is 3 pm

This is exactly what modulo does:

15 / 12 = 1, remainder 3

You find this example better explained on wikipedia: Wikipedia Modulo Article

Answer 5

Easier when your number after the decimal (0.xxx) is short. Then all you need to do is multiply that number with the number after the division.

Ex: 32 % 12 = 8

You do 32/12=2.666666667 Then you throw the 2 away, and focus on the 0.666666667 0.666666667*12=8 <-- That's your answer.

(again, only easy when the number after the decimal is short)

Answer 6

modulus division is simply this : divide two numbers and return the remainder only

27 / 16 = 1 with 11 left over, therefore 27 % 16 = 11

ditto 43 / 16 = 2 with 11 left over so 43 % 16 = 11 too