How to Find if a Number Is Divisible by Another Number

SPEED DIVISIBILITY TEST

How to quickly find if a number is divisible by another number. These are a few simple tests that can help you determine the divisibility of a number.

Important Rules:    A number is (divisible by) –

  • divisible by 2 if its last digit is even i.e. 0,2,4,6,8.

            e.g. 370,    92,    2134,   686,    518   are divisible by 2  (you may verify!)

  • divisible by 3 if the sum of its digits is divisible by 3.

            e.g. 4365 is divisible by 3 since  sum of its digits 4+3+6+5 = 18 is divisible by 3

  • divisible by 4 if its last two digits (taken as a number) is divisible by 4.

            e.g. 7936 is divisible by 4 since 36 is divisible by 4

  • divisible by 5 if its last digit is 0 or 5.

     e.g. both 2345 and 760 are divisible by 5

  • divisible by 6 if its last digit is even and the sum of its digits is divisible by 3.

           e.g. 7242 is divisible by 6 since last digit (2) is even and sum of the digits 

           7+2+4+2=15 is divisible 3

  • for checking divisibility by 7, perform following steps- 
  1. pick up the last digit and multiply it by 2 
  2. then subtract this from the truncated original number
  3.  check if this value is divisible by 7 
  4. alternately continue doing this (steps i & ii) until you get single digit.
  5. if in step iii) answer is yes or in step iv) answer is 0 or ±7, then the given number is divisible by 7 

e.g  let us check for 686 .    68 – 2×6 = 56 which is divisible by 7 hence 686 is divisible by 7 (you may verify!)

  • divisible by 8 if its last three digits (taken as a number) is divisible by 8. 

e.g  let us check for 31528 .    528/8 = 66.  hence 31528 is divisible by 8(you may verify!)

  • divisible by 9 if the sum of its digits is divisible by 9.

e.g. 6435 is divisible by 9 since  sum of its digits 6+4+3+5 = 18 is divisible by 9

  • divisible by 10 if its last digit is 0 .

     e.g. 2760 is divisible by 10 (too obvious!)

  • for checking divisibility by 11, perform following steps- 
  1. find the sum of its digits at odd places 
  2. find the sum of its digits at even places 
  3.  find the difference between two sums found at i) & ii) 
  4. If the difference is 0 or divisible by 11, then the given number is divisible by 11

e.g  let us check for 3841728 .    

(sum of digits at odd places) – (sum of digits at even places) 

= (3+4+7+8) – (8+1+2) = 11 which is divisible by 11. Hence the given number is divisible by 11

Using this guide you can quickly find if a number is divisible by another!