178 LearnersLast updated on May 26th, 2025
Divisibility Rule of 81
The divisibility rule is a way to find out whether a number is divisible by another number without using the division method. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 81.
What is the Divisibility Rule of 81?
The divisibility rule for 81 is a method by which we can find out if a number is divisible by 81 or not without using the division method. Check whether 729 is divisible by 81 with the divisibility rule.
Step 1: Check if the sum of the digits of the number is divisible by 9. For 729, the sum is 7 + 2 + 9 = 18. Since 18 is divisible by 9, proceed to the next step.
Step 2: Divide the number by 9. If the result is still divisible by 9, then the original number is divisible by 81. For 729, 729 ÷ 9 = 81. Since 81 is divisible by 9, 729 is divisible by 81.
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Tips and Tricks for Divisibility Rule of 81
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 81.
Know the multiples of 81:
Memorize the multiples of 81 (81, 162, 243, 324, etc.) to quickly check divisibility.
Use the sum of digits:
If the sum of the digits is not divisible by 9, then the number is not divisible by 81.
Repeat the process for large numbers:
For very large numbers, break them down into parts that can be easily summed up. For example, check if 7290 is divisible by 81 using the divisibility test. The sum of digits is 7 + 2 + 9 + 0 = 18, which is divisible by 9, hence divide 7290 by 9, resulting in 810. Since 810 is divisible by 9, 7290 is divisible by 81.
Use the division method to verify:
Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 81
The divisibility rule of 81 helps us to quickly check if the given number is divisible by 81, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not verifying divisibility by 9 twice.
Students should ensure the number is divisible by 9 two times in succession.
Mistake 2
Miscalculating the sum of digits.
Double-check the addition of digits to ensure accuracy.
Mistake 3
Not repeating the process when the sum is large.
Students often stop the process after reaching a large sum. Break it down further if necessary.
Mistake 4
Confusing the steps.
Regular practice will help students remember and correctly apply the steps.
Mistake 5
Not considering negative values.
Students often ignore negative values, thinking divisibility rules don't apply to them. Divisibility rules apply to negative values as well, so consider negative values as positives when checking divisibility.
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Divisibility Rule of 81 Examples
Problem 1
Is 243 divisible by 81?
Yes, 243 is divisible by 81.
Explanation
To verify if 243 is divisible by 81, we follow these steps:
1) Sum the cubes of the digits: (2^3 + 4^3 + 3^3 = 8 + 64 + 27 = 99).
2) Check if the result, 99, is divisible by 81. It is not, but the sum of cubes of digits for 243 directly gives us 243, which is (81 times 3).
Problem 2
Check the divisibility rule of 81 for 729.
Yes, 729 is divisible by 81.
Explanation
For 729, we apply the rule:
1) Sum the cubes of the digits: (7^3 + 2^3 + 9^3 = 343 + 8 + 729 = 1080).
2) Check if 1080 is divisible by 81. It is not, but the number 729 itself is (81 times 9).
Problem 3
Is 162 divisible by 81?
Yes, 162 is divisible by 81.
Explanation
To check divisibility:
1) Sum the cubes of the digits: (1^3 + 6^3 + 2^3 = 1 + 216 + 8 = 225).
2) Check if 225 is divisible by 81. It is not, but 162 is exactly (81 times 2).
Problem 4
Can 486 be divisible by 81 following the divisibility rule?
Yes, 486 is divisible by 81.
Explanation
For 486, we follow the steps:
1) Sum the cubes of the digits: (4^3 + 8^3 + 6^3 = 64 + 512 + 216 = 792).
2) Check if 792 is divisible by 81. It is not, but 486 itself is (81 times 6).
Problem 5
Check the divisibility rule of 81 for 972.
Yes, 972 is divisible by 81.
Explanation
To check:
1) Sum the cubes of the digits: (9^3 + 7^3 + 2^3 = 729 + 343 + 8 = 1080).
2) Verify if 1080 is divisible by 81. It is not, but 972 is (81 times 12).
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FAQs on Divisibility Rule of 81
1.What is the divisibility rule for 81?
2.How many numbers are there between 1 and 500 that are divisible by 81?
3.Is 324 divisible by 81?
4.What if the sum of digits is 0?
5.Does the divisibility rule of 81 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 81?
7.What are some fun ways kids in India can practice Divisibility Rule of 81 with numbers?
8.What role do numbers and Divisibility Rule of 81 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 81 skills?
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Important Glossaries for Divisibility Rule of 81
- Divisibility rule: A set of guidelines used to determine if a number can be divided by another number without a remainder.
- Multiples: Numbers obtained by multiplying a given number by an integer. For example, multiples of 81 are 81, 162, 243, etc.
- Integers: Whole numbers that include positive numbers, negative numbers, and zero.
- Sum of digits: The total obtained by adding all the digits of a number.
- Verification: The process of confirming whether a calculation or result is accurate, often by using a different method.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
