What is the Divisibility Rule for Class 9?
A number is divisible by 9 if the sum of its digits is divisible by 9.
The divisibility rule for 9 is a simple yet powerful tool for determining whether a number is divisible by 9 without performing actual division. It states:
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Rule: Add all the digits of the number together. If the sum of the digits is divisible by 9, then the original number is also divisible by 9.
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Example 1: Consider the number 729.
- Sum of digits: 7 + 2 + 9 = 18
- 18 is divisible by 9 (18 รท 9 = 2), therefore 729 is divisible by 9.
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Example 2: Consider the number 43533.
- Sum of digits: 4 + 3 + 5 + 3 + 3 = 18
- 18 is divisible by 9, therefore 43533 is divisible by 9.
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Example 3: Consider the number 2613.
- Sum of digits: 2 + 6 + 1 + 3 = 12
- 12 is not divisible by 9, therefore 2613 is not divisible by 9.
This rule applies to numbers of any size. The repeated application of summing digits can simplify the process for very large numbers. If, after summing the digits repeatedly, the result is 9, the original number is divisible by 9.
Many resources confirm this rule including Byju's, CK-12, and Cuemath.
