What Is the Divisibility Rule for 9?


Quick Answer

A number is divisible by 9 if and only if the sum of its digits is divisible by 9. If a number is divisible by 9, it is also divisible by 3 because 9 is a dividend of 3.

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Full Answer

Consider the example of 7425 where the sum of its digits is equal to 18. Since 18 is divisible by 9, 7425 is divisible by 9. The number 7425 is also divisible by 3. However, the reverse is not necessarily true. For instance, the number 33 is divisible by 3 but it is not divisible by 9. The divisibility rule on sum of digits does not work for higher powers of 3. For instance, the sum of the digits of 7425 is 18 but 7425 is not divisible by 18.

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