Divisibility Tests – Continued (Part II)

1. Test for 8 – If the number formed by last 3 digits is divisible by 8 . Ex- In 123456                                                                                                  the number formed by last 3 digits is 456, which is divisible by 8.  So, 123456 is divisible by 8
2. Test for 9 – If sum of digits is divisible by 9.
3. Test for 10 – If unit digit is 0
4. Test for 11 –  If the difference of the sum of the digits in the even places and the sum of digits in odd places is divisible by 11 or 0 .           Ex – 58432 ,   numbers in odd places are    5,4,2    and  numbers  in even places are 8,3( 5+4+2 ) – ( 8+3 ) = 11 – 11 = 0 ,                              so 58432 is divisible by 11 .
5. Test for 12 –If it is divisible by 4&3. Number formed by last 2 digits is divisible by 4 and sum of digits is divisible by 3.                        EX- In 123456  ,  sum of digits  is 1+2+3+4+5+6 = 21 , divisible by3,  number formed by last two digits is 56 , divisible by 4 .                        So, 123456 is divisible by 12.
6. Test for 13 — Method 1 – Multiply unit digit by 9 and subtract it from rest. If the result is divisible by 13 the whole number is divisible by 13.  Ex- IN  559, unit digit is 9 and rest is 55     55 – 9×9 = 55 – 81 = – 26, which is divisible by 13.  So 559 is divisible by 13                                                  Method 2 — Multiple unit digit by 4 and add it to the remaining number.    Ex – 12519 , unit digit is 9 and rest is 1251                                     1251+ 4×9 = 1251 + 36 = 1287 ,  Repeat the same method  for 1287                                                                                                                               128 + 4×7 = 128+28 =156 , which is divisible by 13  .  So, 12519 is divisible by 13

Kiran Bala Dash (Grandmother of Tanay – 4E and Vinay – LKG D).

 Retired Lecturer in Mathematics