18 July 2016

Divisibility Tests by 2, 4, 8, 16, 32 OR 2's any Power

In order to know whether the given DIVIDEND is divisible by the given DIVISOR without actually doing the LONG DIVISION PROCESS we will require certain rules. And these rules are called DIVISIBILITY TESTS.

Read: Complete Concept of Division of Numbers

Divisibility by 2
  • A number whose unit digit or the last digit is an EVEN number then the actual number is divisible by 2.
  • Or you can say if the last digit is a MULTIPLE of  2 like 0, 2, 4, 6 and 8 
  • Or any number whose unit/last digit is divisible by 2 then the actual number must be divisible by 2. For example: 
  • 6258 (last digit 8--an even number that means 6258 is divisible by 2)
  • 52668592 (last digit 2--an even number that means 52668592 is divisible by 2)
Divisibility by 4
  • A number whose last 2 digits form a NUMBER that is divisible by 4 then the actual number must be divisible by 4.
  • The last two digits can be 00, 04, 08, 12, 16, 20, 24....etc. For Example:
  • 4832 (last two digits forms 32, a multiple of 4, that means 4832 must be divisible by 4)
  • 569856 (last two digits forms 56, a multiple of 4, that means 569856 must be divisible by 4)
Divisibility by 8
  • A number whose last 3 digits forms a NUMBER that is divisible by 8 than the actual number must be divisible by 8.
  • The last three digits can be 000, 008, 016, 024, 032, 040....etc. For Example:
  • 236104 (last three digits forms 104 which is divisible by 8, that means 236104 must be divisible by 4)
  • 9317640 (last three digits forms 640 which is divisible by 8, that means 9317640 must be divisible by 8)

Important Observation

During the divisibility test by 2 (power of 2 is 1): we were checking divisibility of the number formed by the last or unit digit by 2.

During the divisibility test by 4 (power of 2 is 2): we were checking divisibility of the number formed by the last 2 digits by 4.

During the divisibility test by 8 (power of 2 is 3): we were checking divisibility of the number formed by the last 3 digits by 8.

So, if you want to check the divisibility of number by 16 (power of 2 is 4) just check the number formed by the last 4 digits of that number 16 and if that 4 digit number is divisible by 16 then the actual number must be divisible by 16.

Similarly, if you want to check the divisibility of a number by 32 (power of 2 is 5), in that case you have to check the divisibility of the number formed by the last 5 digits and if that 5 digits number is divisible by the 32 then the actual number must be divisible by 32.

So, accordingly the divisibility of a number by 64, 128, 256......can be checked by checking the last 6, 7, 8,.....digits number formed from the given number as in the above cases.

Divisibility Series:

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