Divisibility Tests by 3, 5, 10, 11, 25

In the last article we learnt the divisibility rules for 2 or 2's any power like 4, 6, 8 etc. Now, in this article you will learn the rules to check the divisibility of any number by 3, 5, 10, 11 and 25. So, let's start.

Divisibility by 3
  • You just have to total all the digits of the given number and check whether the SUM is divisible by 3 or not.
  • So let me check the divisibility of 32562 by 3.
  • SUM of digits 3+2+5+6+2 = 18 which is a multiple of 3. 
  • That means 32562 is divisible by 3.
Divisibility by 5
  • The given number is divisible by 5 if the last or unit's digit of the given number is 0 (ZERO) or 5. 
  • So accordingly, 32560 and 276325 are divisible by 5. Pretty cool!
Divisibility by 10
  • There is only one rule. The last digit of the given number has to be 0 (ZERO) 
  • Ex. 210, 65280, 31250 are divisible by 10. 
Divisibility by 11
  • If the DIFFERENCE between the SUM OF DIGITS at the EVEN places and the sum of digits at ODD places is either 0 or a MULTIPLE of 11 then the given the number is perfectly divisible by 11.
  • For Ex. 4276 = DIFFERENCE between (3+7) and (4+6) is 0. That means the given number is divisible by 11.
  • Another Ex. 291918 = DIFFERENCE between (2+1+1) and (9+9+8) is 22, a multiple of 11. That means this number is also divisible by 11. 
Divisibility by 25
  • If the last digits of the given number are ZEROS or a multiple of 25. 
  • More clearly, if the last digits are like 00, 25, 50, 75, etc then the given number is completely divisible by 5.
  • For Ex. 3250 and 452675 are perfectly divisible by 5.

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