Divisibility Rule for 9
Divisibility Rule for 9
Divisibility Rule of 9: This rule is used to check whether a number is divisible by 9 or not without performing long division. The rule states that a number is divisible by 9, if the sum of its digits is divisible by 9.
Justification: Let be a two digit number.
Then, n can be written as n = 10a + b, where b is units digit of n.
n = 9a + a + b
n = a multiple of 9 + ( a + b )
n will a multiple of 9, if ( a + b ) is a multiple of 9 as 9a is a multiple of 9.
Thus, a two digit number is divisible by 9, if the sum of its digits is divisible by 9.
This can be generalised for any digit of numbers.
Illustration: Check whether 24163785.is divisible by 9.
Solution: To check whether 24163785 is divisible by 9. We will find the sum of digits.
The sum of the digits of n is 2 + 4 + 1 + 6 + 3 + 7 + 8 + 5 = 36.
This number is divisible by 9. So, n is divisible by 9.
Illustration: Check whether 187525.is divisible by 9.
Solution: To check whether 187525 is divisible by 9. We will find the sum of digits.
The sum of the digits of m is 1 + 8 + 7 + 5 + 2 + 5= 28, which is not divisible by 9. So, m is not divisible by 9.
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