191 LearnersLast updated on May 26th, 2025
Divisibility Rule of 240
The divisibility rule is a way to determine whether a number is divisible by another number without performing actual division. In real life, we can use the divisibility rule for quick calculations, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 240.
What is the Divisibility Rule of 240?
The divisibility rule for 240 is a method to determine if a number is divisible by 240 without using the division method. A number is divisible by 240 if it is divisible by all the prime factors of 240. Since 240 = 2^4 × 3 × 5, a number must be divisible by 16, 3, and 5 to be divisible by 240.
Check whether 480 is divisible by 240 using the divisibility rule.
Step 1: Check divisibility by 16. The last four digits of 480 are 0480, which is divisible by 16.
Step 2: Check divisibility by 3. The sum of the digits in 480 is 4 + 8 + 0 = 12, which is divisible by 3.
Step 3: Check divisibility by 5. The last digit of 480 is 0, which is divisible by 5.
Since 480 is divisible by 16, 3, and 5, it is divisible by 240.
Tips and Tricks for Divisibility Rule of 240
Learning the divisibility rule helps kids master division. Let’s explore a few tips and tricks for the divisibility rule of 240.
Know the prime factorization:
Memorize that 240 = 2^4 × 3 × 5 to quickly check divisibility. A number divisible by 16, 3, and 5 is divisible by 240.
Check divisibility by 16: For divisibility by 16, ensure the last four digits of the number are divisible by 16.
Check divisibility by 3: Sum the digits of the number and check if the sum is divisible by 3.
Check divisibility by 5: Ensure the last digit of the number is either 0 or 5.
Use the division method to verify:
Students can use the division method to verify and crosscheck their results. This will help them learn and confirm their understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 240
The divisibility rule of 240 helps quickly determine if a number is divisible by 240, but common mistakes like calculation errors can lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking all divisibility criteria.
Ensure you check divisibility by 16, 3, and 5, as all are necessary to determine divisibility by 240.
Divisibility Rule of 240 Examples
Problem 1
Does the number of petals on a flower sculpture, 240 petals, allow it to be grouped equally into arrangements of 10, 12, and 20 petals each?
Yes, 240 can be grouped equally into arrangements of 10, 12, and 20 petals.
Explanation
To determine if 240 is divisible by these numbers, we check if it follows the rules for divisibility by 10, 12, and 20:
1) Divisibility by 10: The number ends in 0, so it is divisible by 10.
2) Divisibility by 12: 240 is divisible by both 3 and 4, as the sum of its digits (2 + 4 + 0 = 6) is divisible by 3, and the last two digits (40) are divisible by 4.
3) Divisibility by 20: 240 ends with 0, and 24 (the number formed by removing the last digit) is divisible by 2, so 240 is divisible by 20. Therefore, 240 meets all conditions for divisibility by 240.
Problem 2
A factory produces 240 gadgets in a day. Can these gadgets be packed equally into boxes of 8, 15, and 24 gadgets?
Yes, 240 gadgets can be packed equally into boxes of 8, 15, and 24 gadgets.
Explanation
We need to check if 240 is divisible by 8, 15, and 24:
1) Divisibility by 8: The last three digits of 240 are 240, which is divisible by 8.
2) Divisibility by 15: 240 is divisible by both 3 and 5, as the sum of its digits (6) is divisible by 3, and it ends in 0.
3) Divisibility by 24: 240 is divisible by both 3 and 8, satisfying divisibility by 24. Thus, the factory can pack the gadgets into boxes of these sizes.
Problem 3
A library has 240 books. Can these books be displayed equally on shelves of 6, 10, and 40 books each?
Yes, the 240 books can be displayed equally on shelves of 6, 10, and 40 books.
Explanation
We verify if 240 is divisible by 6, 10, and 40:
1) Divisibility by 6: 240 is divisible by both 2 and 3, as it ends in 0 and the sum of its digits is 6, which is divisible by 3.
2) Divisibility by 10: The number ends in 0, confirming divisibility by 10.
3) Divisibility by 40: The last two digits, 40, are divisible by 4, and the number ends in 0, confirming divisibility by 8 (and thus by 40). Therefore, 240 can be equally displayed on these shelves.
Problem 4
An event planner has 240 chairs. Can these chairs be arranged in equal rows of 5, 12, and 16 chairs each?
Yes, the 240 chairs can be arranged in equal rows of 5, 12, and 16 chairs.
Explanation
We need to ensure 240 is divisible by 5, 12, and 16:
1) Divisibility by 5: 240 ends in 0, so it is divisible by 5.
2) Divisibility by 12: 240 is divisible by both 3 and 4, as the sum of its digits is 6, divisible by 3, and 40 (the last two digits) is divisible by 4.
3) Divisibility by 16: 240 divided by 16 equals 15, which is a whole number, confirming divisibility. Hence, the chairs can be arranged in these rows.
Problem 5
A chef is preparing a feast with 240 cupcakes. Can these cupcakes be served equally on trays of 4, 6, and 20 cupcakes?
Yes, the 240 cupcakes can be served equally on trays of 4, 6, and 20 cupcakes.
Explanation
We check if 240 is divisible by 4, 6, and 20:
1) Divisibility by 4: The last two digits, 40, are divisible by 4.
2) Divisibility by 6: 240 is divisible by both 2 (as it ends in 0) and 3 (sum of digits is 6).
3) Divisibility by 20: 240 ends in 0, and 24 (formed by removing the last digit) is even, confirming divisibility by 20. Thus, the cupcakes can be served on these trays
FAQs on Divisibility Rule of 240
1.What is the divisibility rule for 240?
2.How many numbers are there between 1 and 1000 that are divisible by 240?
3.Is 360 divisible by 240?
4.What if I only check one divisibility rule?
5.Does the divisibility rule of 240 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 240?
7.What are some fun ways kids in United States can practice Divisibility Rule of 240 with numbers?
8.What role do numbers and Divisibility Rule of 240 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 240 skills?
Important Glossaries for Divisibility Rule of 240
- Divisibility rule: A set of rules used to determine whether a number is divisible by another number without performing division.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 240 = 24 × 3 × 5.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, multiples of 240 include 240, 480, 720, etc.
- Integer: A whole number that can be positive, negative, or zero.
- Sum of digits: The total obtained by adding all the digits of a number. Used to check divisibility by 3.
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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.
