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Number System (TEST OF DIVISIBILITY)

TEST OF DIVISIBILITY


  1. Divisibility of 2 : Numbers ending with 0, 2, 4, 6 or 8

  2. Divisibility of 3 : Sum of the digits of the number should be divisible by 3.

Ex . To check whether 3456789 is divisible by 3.

Sol : Divisibility of 3 says

= 3+4+5+6+7+8+9 = 42.

Now, if 42 is divisible by 3 , 3456789 is also divisible by 3 otherwise not.

  1. Divisibility of 4 : Last two digits of the number should be divisible by 4. 

Ex . To check whether 3456782 is divisible by 4.

Sol : Divisibility of 4 says 

If 82 is divisible by 4, 3456782 is divisible by 4

But we can clearly see that, 82 is not divisible by 4 

Hence 3456782 is also not divisible by 4

  1. Divisibility of 5 : Number ending with 0 or 5. 

Ex . To check whether 3451 is divisible by 5.

Sol : We can clearly see that the last digit of the number is 1. 

Hence 3451 is not divisible by 5.

  1. Divisibility of 6 : A number is divisible by 6 if it is divisible by 2 and 3 both. 

Ex . To check whether 3451 is divisible by 6.

Sol : Divisibility of 6 says : Divisible should be by 2 & 3 both

Divisibility of 2 : Number’s Last digit is 1; Hence can’t be divided by 2

Divisibility of 3 : Sum of Digits =  3+ 4+ 5+ 1 = 13 ; again not divisible by 3.

Hence 3451 is not divisible by 6.

  1. Divisibility of 7 : Double the last digit of the number and subtract it from the truncated value and check if the difference is divisible by 7. 

Ex: To check whether 343 is divisible by 7.

Sol : Double the last digit 3*2 = 6

Subtract from the Truncated value = 34 - 6 = 28

Since 28 is divisible by 7.  Hence 343 is divisible by 7.

  1. Divisibility of 8 : Last three digits of the number should be divisible by 8.

Ex: To check whether 34565432 is divisible by 8. 

Sol : Last three digits are 432 which are divisible by 8. 

Hence 34565432 is also divisible by 8.

  1. Divisibility of 9 : Sum of the digits should be divisible by 9.

Ex : To check whether 987654321 is divisible by 9.

Sol : Divisibility of 9 = 9+ 8+ 7+ 6+ 5+ 4+ 3+  2+ 1 = 45

 Since 45 is divisible by 9; Hence 45 is also divisible by 9.

  1. Divisibility of 10 : Last digit of the Number should be 0

  2. Divisibility of 11 : If Difference between the sum of the digits at the ODD places and the digits at the EVEN places  is either 0 or multiple of 11. 

Ex :  To check whether 98765432 is divisible by 11.

Sol : Sum of Even Places = 8 + 6+ 4 + 2 = 20

        Sum of Odd Places = 9 + 7 + 5 + 3 = 24

       Difference of Even and Odd Places = 24 - 20 = 4

4 is not divisible by 11; Hence 98765432 is also not divisible by 11. 

  1. Divisibility of 12 : A number is divisible by 12 if it is divisible by 3 and 4 both.

  2. Divisibility of 15 : A number is divisible by 15 if it is divisible by 3 and 5 both.

  3. Divisibility of 24 : A number is divisible by 24 if it is divisible by 3 and 8 both.

  4. Divisibility of 25 : Last two digits of the number should be 00 or any multiple of 25.

Comments

  1. Unknown19 November 2021 at 12:11

    Thanks mam, these blogs are really very helpful 💐

    ReplyDelete

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