Last updated on May 26th, 2025
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.
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.
Learning the divisibility rule helps kids master division. Let’s explore a few tips and tricks for the divisibility rule of 240.
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.
Students can use the division method to verify and crosscheck their results. This will help them learn and confirm their understanding.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
: She loves to read number jokes and games.