DIVISIBILITY TESTS OF NUMBERS

DIVISIBILITY BY 2 :- A number is divisible by 2 if its ones digit is 0,2,4,6 or 8.
                  For eg.  20, 52, 64, 116, 1988.    { are divisible by 2 }
                              11, 93, 105, 267, 569.    { are not divisible by 2 }

DIVISIBILITY BY 3 :- A number is divisible by 3 only when the sum of its digits is divisible by 3.
                  For eg.  5382                  { consider a number }
                               5+3+8+2 = 18   { sum all the digits }
                              18 is divisible by 3, hence 5382 is divisible by 3.

                               925                     { consider a number }
                               9+2+5 = 16        { sum all the digits }
                               16 is not divisible by 3, hence 925 is not divisible by 3.

DIVISIBILITY BY 4 :- A number is divisibile by 4 if the number formed by the last two digits (ones & tens digit) of the number is divisible by 4.
                  For eg.  7516, 5208, 3212         { last two digits of number is divisible by 4}
                               hence, the numbers are divisible by 4.

DIVISIBILITY BY 5 :- A number is divisible by 5 if the last digit ( ones digit ) of the number is 0 or 5.
                  For eg.  76385       { ones digit is 5 }
                               hence, 76385 is divisible by 5.

DIVISIBILITY BY 6 :- A number is divisible by 6 if the number is divisible by both 2 & 3.
                  For eg.  85332
                               85332  is divisible by 2.
                               8+5+3+3+2 = 21
                               21  is divisible 3                          { 85332 is divisible both 2 & 3 }
                               Hence, 85332 is divisible by 6.

DIVISIBILITY BY 7 :- To test the divisibility of 7, we follow the steps given below-
                                     315             { suppose a number }
                                     5 * 2 = 10    { double the digit in ones place }
                                     31 - 10 = 21 { subtract the number formed, by rest of the digit }
                                     Then if 21 is divisible by 7 then the given number is also divisible by 7.

DIVISIBILITY BY 8 :-  A number is divisible by 8, if the number formed by the last 3 digits ( ones, tens, hundreds  place ) is divisible by 8.
                  For eg.  67696      { consider the last three digits }
                               696 is divisible by 8.
                               hence, 67696 is also divisible by 8.

DIVISIBILITY BY 9 :-  A number is divisible by 9 if the sum of its digits is divisible by 9.
                  For eg.  574263    { suppose a number }
                               5+7+4+2+6+3 = 27     { sum all the digits }
                               27 is divisible by 9.
                               hence, 574263 is also divisible by 9.

DIVISIBILITY BY 10 :-  A number is divisible by 10 only when its unit digit is zero(0).
                    For eg.  7430 is divisible by 10.

DIVISIBILITY BY 11 :-  A number is divisible by 11 if the difference of the sum of its digits at odd places and even places is 0 or multiple of 11.
                    For eg.  64537            { suppose a number }
                                 6+5+7 = 18   { sum of odd place digits}
                                 4+3 = 7         { sum of even place digits}
                                 18 - 7 = 11    { difference }
                                 hence, 64537 is divisible by 11.