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 seem to find an explanation in layman s terms online  Can someone elaborate on a very high level as to what s going on here

User · Accepted Answer

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

User · Answer

27   16   11   You can interpret it this way    16 goes 1 time into 27 before passing it       16   2   32    So you could say that 16 goes one time in 27 with a remainder of 11    In fact        16   11   27   An other exemple       20   3   2    Well 3 goes 6 times into 20 before passing it      3   6   18   To add-up to 20 we need 2 so the remainder of the modulus expression is 2

User · Answer

The modulus operator takes a division statement and returns whatever is left over from that calculation  the  remaining  data  so to speak  such as 13   5   2  Which means  there is 3 left over  or remaining from that calculation  Why  because 2   5   10  Thus  13 - 10   3    The modulus operator does all that calculation for you  13   5   3

User · Answer

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

User · Answer

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  lt -- That s your answer    again  only easy when the number after the decimal is short

User · Answer

Modulus division gives you the remainder of a division  rather than the quotient

User · Answer

When we divide two integers we will have an equation that looks like the following   A B    Q remainder R  A is the dividend  B is the divisor  Q is the quotient and R is the remainder  Sometimes  we are only interested in what the remainder is when we divide A by B  For these cases there is an operator called the modulo operator  abbreviated as mod    Examples  16 5  3 Remainder 1  i e  16 Mod 5 is 1  0 5  0 Remainder 0 i e 0 Mod 5 is 0  -14 5  3 Remainder 1 i e  -14 Mod 5 is 1    See Khan Academy Article for more information   In Computer science  Hash table uses Mod operator to store the element where A will be the values after hashing  B will be the table size and R is the number of slots or key where element is inserted   See How does a hash table works for more information

User · Answer

I would like to add one more thing   it s easy to calculate modulo when dividend is greater larger than divisor  dividend   5 divisor   3     5   3   2   3 5 1   3 -----   2   but what if divisor is smaller than dividend  dividend   3 divisor   5     3   5   3    how    This is because  since 5 cannot divide 3 directly  modulo will be what dividend is

User · Answer

Lets say you have 17 mod 6    what total of 6 will get you the closest to 17  it will be 12 because if you go over 12 you will have 18 which is more that the question of 17 mod 6  You will then take 12 and minus from 17 which will give you your answer  in this case 5   17 mod 6 5

User · Answer

I hope these simple steps will help   20   3   2     20   3   6  do not include the  6667     just ignore it 3   6   18 20 - 18   2  which is the remainder of the modulo

User · Answer

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

User · Answer

It s simple  Modulus operator    returns remainder after integer division  Let s take the example of your question  How 27   16   11  When you simply divide 27 by 16 i e  27 16  then you get remainder as 11  and that is why your answer is 11

User · Answer

Very simple  a   b is defined as the remainder of the division of a by b   See the wikipedia article for more examples

User · Answer

Most explanations miss one important step  let s fill the gap using another example   Given the following   Dividend  16 Divisor  6   The modulus function looks like this   16   6   4   Let s determine why this is   First  perform integer division  which is similar to normal division  except any fractional number  a k a  remainder  is discarded   16   6   2   Then  multiply the result of the above division  2  with our divisor  6    2   6   12   Finally  subtract the result of the above multiplication  12  from our dividend  16    16 - 12   4   The result of this subtraction  4  the remainder  is the same result of our modulus above

User · Answer

Modulus division is pretty simple  It uses the remainder instead of the quotient       1 0833     lt -- Quotient       12 13    12     1  lt -- Remainder     1 00  lt -- Remainder can be used to find decimal values       96       040       036       0040  lt -- remainder of 4 starts repeating here  so the quotient is 1 083333      13 12   1R1  ergo 13 12   1     It helps to think of modulus as a  cycle    In other words  for the expression n   12  the result will always be  lt  12   That means the sequence for the set 0  100 for n   12 is    0 1 2 3 4 5 6 7 8 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 0       4    In that light  the modulus  as well as its uses  becomes much clearer

User · Answer

The only important thing to understand is that modulus  denoted here by   like in C  is defined through the Euclidean division    For any two  d  q  integers the following is always true   d     d   q     q     d   q     As you can see the value of d q depends on the value of d q  Generally for positive integers d q is truncated toward zero  for instance 5 2 gives 2  hence   5    5 2  2    5 2    gt  5   2 2    5 2    gt  5 2   1   However for negative integers the situation is less clear and depends on the language and or the standard  For instance -5 2 can return -2  truncated toward zero as before  but can also returns -3  with another language     In the first case    -5    -5 2  2    -5 2    gt  -5   -2 2    -5 2    gt  -5 2   -1   but in the second one    -5    -5 2  2    -5 2    gt  -5   -3 2    -5 2    gt  -5 2    1   As said before  just remember the invariant  which is the Euclidean division   Further details     What is the behavior of integer division  Division and Modulus for Computer Scientists

User · Answer

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

User · Answer

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

User · Answer

This was the best approach for me for understanding modulus operator  I will just explain to you through examples   16   3   When you division these two number  remainder is the result  This is the way how i do it   16   3   3   3   6  6   3   9  9   3   12  12   3   15   So what is left to 16 is 1  16   3   1   Here is one more example  16   7   7   7   14 what is left to 16  Is 2 16   7   2  One more  24   6   6   6   12  12   6   18  18   6   24  So remainder is zero  24   6   0

[language-agnostic] How Does Modulus Divison Work

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