169 LearnersLast updated on May 26th, 2025
Divisibility Rule of 117
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 117.
What is the Divisibility Rule of 117?
The divisibility rule for 117 is a method by which we can find out if a number is divisible by 117 or not without using the division method. Check whether 4095 is divisible by 117 with the divisibility rule.
Step 1: Break down the number 117 into its prime factors: 117 = 3 × 39.
Step 2: Check the divisibility of the number for each of the factors.
- For 3: Add all the digits of the number. If the sum is a multiple of 3, then the number is divisible by 3. For 4095, 4 + 0 + 9 + 5 = 18, and 18 is a multiple of 3.
- For 39: Check if the number is divisible by 39 using either direct division or by applying divisibility rules for 3 and 13, since 39 = 3 × 13.
Step 3: If the number is divisible by both 3 and 39, then it is divisible by 117. Since 4095 satisfies these conditions, it is divisible by 117.
Tips and Tricks for Divisibility Rule of 117
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 117.
Know the multiples of 117:
Memorize the multiples of 117 (117, 234, 351, 468, etc.) to quickly check divisibility. If a number is a multiple of 117, then it is divisible by 117.
Use prime factorization:
By understanding the prime factorization of 117, you can apply known divisibility rules for smaller factors like 3 and 39 to simplify the process.
Repeat the process for large numbers:
For large numbers, continue checking divisibility by breaking down into smaller factors until you reach a number divisible by 117.
Use the division method to verify:
Students can use the division method as a way to verify and crosscheck their results, ensuring they have applied the rule correctly.
Common Mistakes and How to Avoid Them in Divisibility Rule of 117
The divisibility rule of 117 helps us to quickly check if a given number is divisible by 117, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps by checking divisibility through prime factorization and ensuring each factor's rule is applied correctly.
Divisibility Rule of 117 Examples
Problem 1
Is 2340 divisible by 117?
Yes, 2340 is divisible by 117.
Explanation
To check the divisibility of 2340 by 117, follow these steps:
1) Break down the number into smaller parts that can be easily verified. Let's try dividing 2340 by 3 (since 117 is divisible by 3) to simplify.
2) 2340 divided by 3 is 780.
3) Now check if 780 is divisible by 39 (since 117 = 3 x 39).
4) 780 divided by 39 is 20, which is an integer, confirming that 2340 is divisible by 117.
Problem 2
Check the divisibility rule of 117 for 702.
Yes, 702 is divisible by 117.
Explanation
To verify the divisibility of 702 by 117, use these steps:
1) Recognize that 702 is a product of smaller factors. First, check divisibility by 9 (since 117 is divisible by 9).
2) The sum of the digits of 702 is 7 + 0 + 2 = 9, which is divisible by 9.
3) Now, check if the result is divisible by 13 (since 117 = 9 x 13). 702 divided by 13 is 54.
4) Since 54 is an integer, 702 is divisible by 117.
Problem 3
Is -351 divisible by 117?
Yes, -351 is divisible by 117.
Explanation
To check if -351 is divisible by 117, ignore the negative sign and follow these steps:
1) Calculate 351 divided by 3 (since 117 is a multiple of 3). The result is 117.
2) Now, 117 divided by 117 equals 1, which is an integer.
3) Therefore, -351 is divisible by 117.
Problem 4
Can 580 be divisible by 117 following the divisibility rule?
No, 580 is not divisible by 117.
Explanation
To verify, follow these steps:
1) Check if 580 is divisible by 3. The sum of the digits is 5 + 8 + 0 = 13, which is not divisible by 3.
2) Therefore, 580 does not meet the necessary condition for divisibility by 117 (since 117 is a multiple of 3).
3) Thus, 580 is not divisible by 117.
Problem 5
Check the divisibility rule of 117 for 819.
Yes, 819 is divisible by 117.
Explanation
To confirm, follow these steps:
1) Check if 819 is divisible by 9. The sum of the digits is 8 + 1 + 9 = 18, which is divisible by 9.
2) Next, check divisibility by 13. 819 divided by 13 is 63, which is an integer.
3) Since both conditions are met, 819 is divisible by 117.
FAQs on Divisibility Rule of 117
1.What is the divisibility rule for 117?
2.How many numbers are there between 1 and 1000 that are divisible by 117?
3.Is 351 divisible by 117?
4.What if I get 0 after checking all factors?
5.Does the divisibility rule of 117 apply to all integers?
6.How can children in Vietnam use numbers in everyday life to understand Divisibility Rule of 117?
7.What are some fun ways kids in Vietnam can practice Divisibility Rule of 117 with numbers?
8.What role do numbers and Divisibility Rule of 117 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Divisibility Rule of 117 skills?
Important Glossaries for Divisibility Rule of 117
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Prime factorization: The expression of a number as the product of its prime factors.
- Multiples: The results we get after multiplying a number by an integer.
- Integers: The numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by reducing one number from 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.
