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

By which number 23973 is divisible

Right Option : B
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Question : 2

Which number is divisible by 4 and 9?

Right Option : C
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Explanation
Question : 3

Which of the following numbers are divisible by 9:

1. 497655

2. 342598

3. 226539

4. 929546

Right Option : D
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Explanation
 
 


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