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

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
Question : 2

Which of the following number is divisible by 9 ?

352,788,435,687

Right Option : C
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Explanation
Question : 3

Replace by a  digit so that the number is divisible by 9.

1______ 80498

Right Option : B
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Explanation
 
 


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