199 LearnersLast updated on May 26th, 2025
Divisibility Rule of 369
The divisibility rule is a way to determine whether a number is divisible by another number without performing division. In real life, we can use the divisibility rule for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 369.
What is the Divisibility Rule of 369?
The divisibility rule for 369 is a method by which we can determine if a number is divisible by 369 without using division. Check whether 1107 is divisible by 369 with the divisibility rule.
Step 1: Check if the number is divisible by both 3 and 9. To be divisible by 3, the sum of the digits must be a multiple of 3. To be divisible by 9, the sum of the digits must also be a multiple of 9.
Step 2: For 1107, add the digits: 1 + 1 + 0 + 7 = 9. Since 9 is divisible by both 3 and 9, proceed to the next step.
Step 3: Now check if the number is divisible by 41. Divide 1107 by 41. If the quotient is a whole number, then 1107 is divisible by 369. In this case, 1107 ÷ 41 = 27, which is a whole number.
Therefore, 1107 is divisible by 369.
Tips and Tricks for Divisibility Rule of 369
Learning divisibility rules will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 369.
- Know the multiples of 369: Memorize the multiples of 369 (369, 738, 1107, etc.) to quickly check divisibility. If the result of the division is a whole number, then the number is divisible by 369.
- Use the divisibility rules for 3 and 9: Since divisibility by 369 requires divisibility by both 3 and 9, always start by checking these two rules. If a number fails either test, it is not divisible by 369.
- Practice with smaller numbers: Begin with smaller numbers to understand the concept before moving on to larger numbers.
- Verify with division: Always use the division method to verify and cross-check your results. This will help ensure accuracy and reinforce learning.
Common Mistakes and How to Avoid Them in Divisibility Rule of 369
The divisibility rule of 369 helps us quickly check if a number is divisible by 369, but common mistakes like calculation errors can lead to incorrect conclusions. Here, we will understand some common mistakes and their solutions.
Mistake 1
Ignoring divisibility by 3 and 9.
Always check that the number is divisible by both 3 and 9 before proceeding to check divisibility by 41.
Mistake 2
Not verifying the result with actual division.
Use long division to confirm that the number is divisible by 369.
Mistake 3
Confusing the steps.
Practice regularly to remember the steps and avoid confusion.
Mistake 4
Assuming a number divisible by 3 and 9 is automatically divisible by 369.
Remember to check divisibility by 41 separately after confirming divisibility by 3 and 9.
Mistake 5
Forgetting to practice regularly.
Regular practice will help reinforce the steps and improve accuracy.
Divisibility Rule of 369 Examples
Problem 1
Is the number of pages in a book, which is 738, divisible by 369?
Yes, 738 is divisible by 369.
Explanation
To check if 738 is divisible by 369, we use the divisibility rule.
1) Sum the digits of the number: 7 + 3 + 8 = 18.
2) Since 18 is a multiple of 9, we check further by dividing the number by 369.
3) 738 ÷ 369 = 2, which is a whole number. Therefore, 738 is divisible by 369.
Problem 2
A factory produces 1107 widgets in one day. Is this number divisible by 369?
Yes, 1107 is divisible by 369.
Explanation
To verify divisibility of 1107 by 369, follow these steps:
1) Sum the digits: 1 + 1 + 0 + 7 = 9.
2) Since 9 is a multiple of 9, check further by dividing by 369.
3) 1107 ÷ 369 = 3, which is a whole number. Thus, 1107 is divisible by 369.
Problem 3
A conference hall has a seating capacity of 1845 seats. Can this number be evenly divided by 369?
No, 1845 is not divisible by 369.
Explanation
To determine if 1845 is divisible by 369, the procedure is:
1) Sum the digits: 1 + 8 + 4 + 5 = 18.
2) Since 18 is a multiple of 9, attempt division by 369.
3) 1845 ÷ 369 = 5.0008, which is not a whole number. Therefore, 1845 isn't divisible by 369.
Problem 4
An artist has 1476 paintbrushes. Is this number divisible by 369?
No, 1476 is not divisible by 369.
Explanation
To check divisibility of 1476 by 369, follow the steps:
1) Sum the digits: 1 + 4 + 7 + 6 = 18.
2) Since 18 is a multiple of 9, try dividing by 369.
3) 1476 ÷ 369 = 4, but rechecking shows a decimal, indicating it's not perfectly divisible. So, 1476 is not divisible by 369.
Problem 5
A bakery made 3690 cookies today. Is this total divisible by 369?
Yes, 3690 is divisible by 369.
Explanation
To determine divisibility by 369, use the steps:
1) Sum the digits: 3 + 6 + 9 + 0 = 18.
2) Since 18 is a multiple of 9, divide by 369 to check.
3) 3690 ÷ 369 = 10, which is a whole number. Therefore, 3690 is divisible by 369.
FAQs on Divisibility Rule of 369
1.What is the divisibility rule for 369?
2.How many numbers are there between 1 and 1500 that are divisible by 369?
3.Is 1107 divisible by 369?
4.Do I need to check divisibility by 41 if a number is divisible by 3 and 9?
5.Does the divisibility rule of 369 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 369?
7.What are some fun ways kids in United States can practice Divisibility Rule of 369 with numbers?
8.What role do numbers and Divisibility Rule of 369 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 369 skills?
Important Glossaries for Divisibility Rule of 369
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number without division.
- Multiple: A number that can be divided by another number without leaving a remainder.
- Integer: A whole number that can be positive, negative, or zero.
- Sum: The result of adding two or more numbers.
- Quotient: The result obtained by dividing one number by another.
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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.
