Divisibility Rule of 9


 
 
Concept Explanation
 

Divisibility Rule of 9

Divisibility Rule of 9:

A number is divisible by 9, if the sum of its digits is divisible by 9.

Justification:

Let us first consider case of a two digit number:

 n=overline{ab} be a two digit number. Then, n can be written as

         n = 10a + b, where b is units digit of n.

Rightarrow    n = 9a + a + b

Rightarrow    n = a multiple of 9 + ( a + b )

Rightarrow    n is a multiple of 9, if ( a + b ) is a multiple of 9

Thus, a two digit number is divisible by 9, if the sum of its digits is divisible by 9.

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Sample Questions
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Question : 1

Which of the following is  not divisble by 9 ?

Right Option : C
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Question : 2

A 6 digit number begins with the digit 8. The number is divisible by 9. All the digits of the number are different. What is the smallest possible value of this number?

Right Option : B
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Question : 3

Consider the following statements and choose the correst option (s) for them.

I. A number divisible by 3 is also divisible by 9.

II. A number divisible by 3 and by 9, if the sum of all its digits can be divided by 3 and by 9, respectively.

Right Option : B
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Explanation
 
 


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