The divisibility rule of 9 states that if the sum of digits of any number is divisible by 9, then the number is also divisible by 9. Divisibility by 9 is a rule that allows us to find whether a number is divisible by 9 or not without performing long division. The divisibility rule of 9 helps us to find whether a number is a multiple of 9 or not without performing the actual division.
Some of the multiples of 9 are 9, 18, 27, 36, 45, etc. Do you see a common pattern in the sum of the digits of these numbers? The sum of digits of all these numbers is itself a multiple of 9.
So, as per the divisibility test of 9, if the sum of all the digits of a number is a multiple of 9, then the number is also divisible by 9. There is a fun activity based on the divisibility rule of 9. Ask your friend to think of any single-digit non-zero number.
Then you can find out what the other digit of the number is, by using the divisibility test of 9. The other digit can be obtained by subtracting the known digit from 9.
Let's try it out with a number, let's say 6. Three times 6 is Now, multiply 18 by 3, which is If we know any one of the digits, let's say 4, we can easily find out what is the other digit by subtracting it from 9, i. So, the other digit is 5. With large numbers also, the rule is the same.
The only difference is that we use the divisibility test of 9 repeate dly until we get the sum of the digits of the number closer to 9. So, is not divisible by 9. Let us take another example. So, is divisible by 9. Let us look at the steps to apply the divisibility rule of 9 easily with any large or smaller numbers:.
Both the divisibility test of 9 and 3 are based on the same principle, which states that the sum of the digits of the given number should be divisible by them. To check if a number is divisible by 3 or not, the sum of all the digits of the number should be divisible by 3, while on the other hand in the case of divisibility rule by 9, if the sum of all the digits of the number is divisible by 9, then the number is also a multiple of 9. For example, to find whether is divisible by 9 and 3 or not, let us find the sum of the digits.
The sum '9' is divisible by both 9 and 3, therefore, is divisible by both 9 and 3. Here, one important fact is that every number which is divisible by 9 is also divisible by 3 because 9 is itself a multiple of 3.
On the other hand, every number which is divisible by 3 may or may not be divisible by 9. We have already discussed the divisibility rule of 9, so here let's understand the divisibility by It is by finding the difference of the sum of digits at even places and at odd places.
Both the rules are based on the sum of digits, but in the case of 11, we have to find the sum of digits at odd place values and at even place values separately, and then if the difference between the two sums is divisible by 11, the number will also be divisible by For example, let us find whether is divisible by 9 and 11 or not.
So, is divisible by both 9 and We are using decimal notation and have our digit symbols. Sign up to join this community.
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