Know the various problems on Divisibility Rules of 9 and get their solutions here. Follow the steps to divide a number by 9 and also know the cases in which it is divisible. Refer to various tricks and terms used in Divisibility Rules of 9 and make your practice efficient. Compare the problems with real-life situations and make the process easy. Refer to the entire article and become perfect in the concepts of divisibility test by 9, formulae, etc..
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Divisible by 9 | Test of Divisibility
The divisibility rule of 9 is the same as rule 3. The small technique to know if the digits are divisible by 9 is that we have to find the sum of digits and check if it is divisible by 9, then the number itself will be divided by the number 9.
For example, 83683 is the number, the sum of the digits is 28 which is not divisible by 9. Therefore, the number 83683 is also not divisible by 9.
How to find if the number is divisible by 9?
Condition 1: If it is a single-digit number
Step 1: In this step, we have to find if the number is a single digit.
Step 2: If the number is a single digit, then check if it is the multiple of 9.
Step 3: If it is a multiple of 9, then the number is divisible by 9 and the condition satisfies.
Else, If it is not a multiple of 9, then it is considered as the number that is not divisible by 9.
Condition 2: If it is a two-digit number
Step 1: If the number is of two digits, then we have to check if it is a direct multiple of 9.
Step 2: If it is a multiple of 9, then the number is divisible by 9 and the condition satisfies.
Else, If it is not the direct multiple of 9, then we have to follow the procedure given in the next step.
Step 3: In this step, we have to add the digits of a number.
Step 4: Now find if that resultant sum is divisible by 9.
Step 5: If the resultant sum is “9”, then the number is divisible by 9 and the condition satisfies.
Else, If the resultant sum is not “9”, then it is considered as the number that is not divisible by 9.
Condition 3: For numbers having more than two digits (Eg: 3, 4, or 5 digits)
The same procedure as of “Condition 2” should be followed for numbers having more than 2 digits.
Important Points to know if a number is divisible by 9
- If it is said that the number is divisible by 9, then it means that it is exactly divided by 9 and leaves the remainder as 0.
- A number is said to be divisible by 9, only and if its sum of digits is divisible by 9.
- This technique works for all the numbers no matter how large they are.
- If the resultant sum of digits is not a multiple of 9, then the number is either a multiple of 9 and hence it is not divisible of 9.
List of Numbers below 100 that are divisible by 9
There are 11 numbers below 100 which are divisible by 9. They are 9(nine), 18(eighteen), 27(twenty seven), 36(thirty six), 45(forty five), 54(fifty four), 63(sixty three), 72(seventy two), 81(eighty one), 90(ninety) and 99(ninety nine).
The other numbers apart from these 11 numbers are not divisible by 9.
Divisibility Test by 9 Examples
Problem 1:
Find if the number 467532 is divisible by 9?
Solution:Â
Step 1: In the first step, you have to find if the number is a single-digit number.
As the number is 467532, it is not a single digit.
Step 2: If the number is not a single digit, then you must add all the digits.
In this step, we have to add each digit of number 467532.
i.e., 4 + 6 + 7 + 5 + 3 + 2 = 27
Step 3: If the resultant value is a two-digit number, then add those digits also
As the resultant sum is 27, we have to add both the digits
i.e, 2 + 7 = 9
Step 4: Check if the resultant number is a multiple of 9 or the number 9
The resultant number is 9
Step 5: If it is 9 or multiple of 9, consider the number as it is divisible by 9
The resultant number is 9, then it is considered as the number that is divisible by 9
By following all the steps above, we consider that 467532 is divisible by 9.
Example 2:
Find if the number 572563 is divisible by 9?
Solution:
Step 1: In the first step, you have to find if the number is a single-digit number.
As the number is 572563, it is not a single digit.
Step 2: If the number is not a single digit, then you must add all the digits.
In this step, we have to add each digit of number 572563.
i.e., 5 + 7 + 2 + 5 + 6 + 3 = 28
Step 3: If the resultant value is a two-digit number, then add those digits also
As the resultant sum is 28, we have to add both the digits
i.e, 2 + 8 = 10
Step 4: Check if the resultant number is a multiple of 9 or the number 9
The resultant number is 10
Step 5: If it is not 9 or multiple of 9, consider the number as it is not divisible by 9
The resultant number is 10, then it is considered as the number that is not divisible by 9
Example 3:
Find if the number 74 is divisible by 9?
Solution:
Step 1: In the first step, you have to find if the number is a single-digit number.
As the number is 74, it is not a single digit.
Step 2: If the number is not a single digit, then you must add all the digits.
In this step, we have to add each digit of the number 74.
i.e., 7 + 4 = 11
Step 3: If the resultant value is a two-digit number, then add those digits also
As the resultant sum is 11, we have to add both the digits
i.e, 1+ 1 = 2
Step 4: Check if the resultant number is a multiple of 9 or the number 9
The resultant number is 2
Step 5: If it is not 9 or multiple of 9, consider the number as it is not divisible by 9
The resultant number is 2, then it is considered as the number that is not divisible by 9
See More Divisibility Rules Related Articles:
| Divisible by 2 | Divisible by 3 | Divisible by 4 |
| Divisible by 5 | Divisible by 6 | Divisible by 7 |
| Divisible by 8 | Divisible by 10 |