197 LearnersLast updated on May 26th, 2025
Divisibility Rule of 261
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 261.
What is the Divisibility Rule of 261?
The divisibility rule for 261 is a method by which we can find out if a number is divisible by 261 or not without using the division method. Check whether 522 is divisible by 261 with the divisibility rule.
Step 1: Check if the number is divisible by 3. Add the digits of the number: 5+2+2=9. Since 9 is divisible by 3, proceed to the next step.
Step 2: Check if the number is divisible by 87. Use the divisibility rule for 87, which involves checking divisibility by 3 and 29. We already know 522 is divisible by 3.
Step 3: Now, check if 522 is divisible by 29. Divide 522 by 29. If the result is a whole number, then 522 is divisible by 29. In this case, 522 divided by 29 equals 18, which is a whole number. Therefore, 522 is divisible by 29.
Since 522 is divisible by both 3 and 29, it is divisible by 261.
Tips and Tricks for Divisibility Rule of 261
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 261.
Know the multiples of 261:
Memorize the multiples of 261 (261, 522, 783, etc.) to quickly check the divisibility. If the result from the division is a multiple of 261, then the number is divisible by 261.
Use smaller divisibility checks:
Since 261 is made up of 3 and 87, you can check divisibility by these smaller numbers first.
Break down complex calculations:
For larger numbers, break down the divisibility check into smaller steps using the factors of 261.
Use the division method to verify:
Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 261
The divisibility rule of 261 helps us to quickly check if a given number is divisible by 261, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you avoid errors.
Mistake 1
Not checking divisibility by smaller factors.
Always check divisibility by 3 and 87 first, as they are factors of 261.
Mistake 2
Miscalculating the sum of digits for divisibility by 3.
Ensure you accurately sum all digits of the number for checking divisibility by 3.
Mistake 3
Not verifying divisibility by 29.
Use long division or a calculator to verify if the number is divisible by 29 after checking for 3.
Mistake 4
Forgetting to check all necessary factors.
Remember that for 261, you must check divisibility by both 3 and 87, which includes checking for divisibility by 29.
Mistake 5
Confusing the steps.
Practice regularly to become familiar with the correct steps for checking divisibility by 261.
Divisibility Rule of 261 Examples
Problem 1
Is 783 divisible by 261?
Yes, 783 is divisible by 261.
Explanation
To check if 783 is divisible by 261, we will use a similar approach for divisibility:
1) Split the number into three equal parts: 7, 8, 3.
2) Add the three parts: 7 + 8 + 3 = 18.
3) Check if 18 is divisible by 3, since 3 is a factor of 261. Yes, 18 is divisible by 3 (3 × 6 = 18).
Since 18 is divisible by 3, 783 is divisible by 261.
Problem 2
Check the divisibility rule of 261 for 1044.
Yes, 1044 is divisible by 261.
Explanation
For checking the divisibility rule of 261 for 1044:
1) Split the number into parts: 10, 4, 4.
2) Add the parts: 10 + 4 + 4 = 18.
3) Check if 18 is divisible by 3. Yes, 18 is divisible by 3 (3 × 6 = 18).
Since the sum is divisible by 3, 1044 is divisible by 261.
Problem 3
Is -522 divisible by 261?
Yes, -522 is divisible by 261.
Explanation
To check if -522 is divisible by 261, disregard the negative sign and check the divisibility:
1) Split into parts: 5, 2, 2.
2) Add the parts: 5 + 2 + 2 = 9.
3) Check if 9 is divisible by 3. Yes, 9 is divisible by 3 (3 × 3 = 9).
Since 9 is divisible by 3, -522 is divisible by 261.
Problem 4
Can 1305 be divisible by 261 following the divisibility rule?
No, 1305 is not divisible by 261.
Explanation
To check divisibility by 261:
1) Split into parts: 13, 0, 5.
2) Add the parts: 13 + 0 + 5 = 18.
3) Check if 18 is divisible by 3. Yes, 18 is divisible by 3.
However, dividing 1305 by 261 gives a non-integer result, so it’s not directly divisible by 261 despite the divisibility of the sum by 3.
Problem 5
Check the divisibility rule of 261 for 1566.
Yes, 1566 is divisible by 261.
Explanation
For checking divisibility by 261:
1) Split the number into parts: 15, 6, 6.
2) Add the parts: 15 + 6 + 6 = 27.
3) Check if 27 is divisible by 3. Yes, 27 is divisible by 3 (3 × 9 = 27).
Since 27 is divisible by 3, 1566 is divisible by 261.
FAQs on Divisibility Rule of 261
1.What is the divisibility rule for 261?
2.How many numbers are there between 1 and 1000 that are divisible by 261?
3.Is 783 divisible by 261?
4.What if I get 0 after division?
5.Does the divisibility rule of 261 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 261?
7.What are some fun ways kids in United States can practice Divisibility Rule of 261 with numbers?
8.What role do numbers and Divisibility Rule of 261 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 261 skills?
Important Glossaries for Divisibility Rule of 261
- Divisibility Rule: The set of rules used to determine if a number is divisible by another number.
- Multiples: Results obtained by multiplying a number by an integer. Multiples of 261 include 261, 522, and 783.
- Factors: Numbers that divide another number without leaving a remainder. For 261, factors include 3 and 87.
- Integer: A number that includes all whole numbers, negative numbers, and zero.
- Long Division: A method of dividing numbers to find out if one number is divisible by another, often used for verifying divisibility.
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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.
