# Divisibility Tests – Continued (Part II)

**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**Test for 9**– If sum of digits is divisible by 9.**Test for 10**– If unit digit is 0**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 .**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.**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 **