184 LearnersLast updated on May 26th, 2025
Divisibility Rule of 216
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 216.
What is the Divisibility Rule of 216?
The divisibility rule for 216 is a method by which we can find out if a number is divisible by 216 or not without using the division method. Check whether 432 is divisible by 216 with the divisibility rule.
Step 1: Check the divisibility by 8. Since 216 is 8×27, the rule for 8 is that the last three digits of the number should form a number divisible by 8. Here, 432 is divisible by 8 (432 ÷ 8 = 54).
Step 2: Check the divisibility by 27. Sum the digits of the number and see if the result is divisible by 9. If so, check if the number is divisible by 27. Adding the digits of 432 (4 + 3 + 2 = 9), we find that 9 is divisible by 9. Check if 432 is divisible by 27 (432 ÷ 27 = 16).
Step 3: Since 432 is divisible by both 8 and 27, it is divisible by 216.
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Tips and Tricks for Divisibility Rule of 216
Learn divisibility rules to help kids master the division. Let’s learn a few tips and tricks for the divisibility rule of 216.
Know the multiples of 216:
Memorize the multiples of 216 (216, 432, 648, 864, etc.) to quickly check the divisibility.
Use the rules for 8 and 27:
Ensure the number is divisible by both 8 and 27. A number divisible by 216 must meet both conditions.
Repeat the process for large numbers:
Keep repeating the divisibility process until you reach a smaller number that is clearly divisible by 216.
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 216
The divisibility rule of 216 helps us quickly check if a number is divisible by 216, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not following both steps.
Students should ensure they check divisibility by both 8 and 27, as both are required for divisibility by 216.
Mistake 2
Forgetting to check divisibility by 27.
: Remember that checking divisibility by 8 is not enough; you must also verify divisibility by 27.
Mistake 3
Not repeating the process when the result is unclear.
Continue the process if the divisibility is not apparent after initial checks.
Mistake 4
Confusing the rules for 8 and 27.
Practice each rule separately until you’re comfortable combining them for divisibility by 216.
Mistake 5
Miscalculating the sum of digits for divisibility by 9.
Ensure accurate addition of digits and check for divisibility by 9 before confirming divisibility by 27.
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Divisibility Rule of 216 Examples
Problem 1
Is the number of pages in a book, 432, divisible by 216?
Yes, 432 is divisible by 216.
Explanation
To check if 432 is divisible by 216, we look for divisibility:
1) Divide the number 432 by 216, 432 ÷ 216 = 2.
2) The result is a whole number, so 432 is divisible by 216.
Problem 2
A shipment of 864 items needs to be packed into boxes, each holding 216 items. Can the items be packed evenly?
Yes, 864 items can be packed evenly into boxes of 216 items each.
Explanation
To determine if 864 can be evenly packed into boxes of 216, we perform the division:
1) Divide 864 by 216, 864 ÷ 216 = 4.
2) The result is a whole number, so 864 is divisible by 216.
Problem 3
A theater has 648 seats. Can they be arranged into sections of 216 seats each?
Yes, 648 seats can be arranged into sections of 216 each.
Explanation
To check if 648 seats can be divided into sections of 216:
1) Divide 648 by 216, 648 ÷ 216 = 3.
2) The result is a whole number, indicating 648 is divisible by 216.
Problem 4
Is the distance of 972 kilometers divisible by 216, perhaps for planning rest stops?
Yes, 972 kilometers is divisible by 216.
Explanation
To verify if 972 is divisible by 216:
1) Divide 972 by 216, 972 ÷ 216 = 4.5.
2) The result is not a whole number, indicating 972 is not evenly divisible by 216.
Problem 5
A company is distributing 1080 promotional items evenly across locations, each receiving 216 items. Is this distribution possible?
No, 1080 items cannot be distributed evenly with each location receiving 216 items.
Explanation
To check if 1080 can be divided into groups of 216:
1) Divide 1080 by 216, 1080 ÷ 216 = 5.
2) The result is not a whole number, indicating 1080 is not evenly divisible by 216.
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FAQs on Divisibility Rule of 216
1.What is the divisibility rule for 216?
2.How many numbers are there between 1 and 1000 that are divisible by 216?
3. Is 648 divisible by 216?
4.What if I get 0 after checking divisibility?
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Important Glossaries for Divisibility Rule of 216
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing full division.
- Multiples: The results we get after multiplying a number by an integer. For example, multiples of 216 are 216, 432, 648, etc.
- Sum of digits: The total obtained by adding all the digits in a number.
- Integers: Numbers that include all whole numbers, negative numbers, and zero.
- Division method: The mathematical operation of dividing one number by another to verify 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.
