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

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.