120 LearnersLast updated on May 26th, 2025
Divisibility Rule of 54
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 54.
What is the Divisibility Rule of 54?
The divisibility rule for 54 is a method by which we can find out if a number is divisible by 54 or not without using the division method. Check whether 540 is divisible by 54 with the divisibility rule.
Step 1: Check if the number is divisible by both 2 and 27 (since 54 = 2 × 27).
For divisibility by 2, the number must be even. Since 540 is even, it is divisible by 2.
Step 2: For divisibility by 27, sum the digits of the number repeatedly until you get a single digit. If the result is 9, the number is divisible by 27.
Summing the digits of 540: 5 + 4 + 0 = 9.
Since 9 is a multiple of 9, 540 is divisible by 27.
Step 3: Since 540 is divisible by both 2 and 27, it is divisible by 54.
Tips and Tricks for the Divisibility Rule of 54
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 54.
- Know the multiples of 54: Memorize the multiples of 54 (54, 108, 162, 216, etc.) to quickly check divisibility. If the number is a multiple of both 2 and 27, it is divisible by 54.
- Use repetition for large numbers: Repeat the digit sum process for large numbers until you reach a small number to check divisibility by 27.
For example: Check if 1458 is divisible by 54 using the divisibility test.
Sum the digits of 1458: 1 + 4 + 5 + 8 = 18.Sum the digits of 18: 1 + 8 = 9.
Since 9 is a multiple of 9 and 1458 is even, 1458 is divisible by 54.
- Use the division method to verify: Use the division method to verify and cross-check your results.
Common Mistakes and How to Avoid Them in the Divisibility Rule of 54
The divisibility rule of 54 helps us quickly check if the given number is divisible by 54, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking divisibility by both factors (2 and 27).
Ensure you check divisibility by both 2 and 27.
Mistake 2
Incorrectly summing digits for divisibility by 27.
Double-check your digit addition and ensure the final sum is a multiple of 9.
Mistake 3
Forgetting to verify evenness for divisibility by 2.
Always check if the number is even before proceeding.
Mistake 4
Not repeating the digit sum process for large numbers.
Continue summing digits until you reach a single-digit result.
Mistake 5
Confusing the steps of the rule.
Practice regularly to remember the steps.
Divisibility Rule of 54 Examples
Problem 1
Is 162 divisible by 54?
Yes, 162 is divisible by 54.
Explanation
To check the divisibility of 162 by 54, we can break it down:
1) Check if 162 is divisible by 2 and 27 (since 54 = 2 x 27).
2) 162 is even, so it's divisible by 2.
3) For divisibility by 27, add the digits of 162: 1 + 6 + 2 = 9, which is not a multiple of 27. Therefore, we need to check directly by division: 162 ÷ 54 = 3, which is an integer. Thus, 162 is divisible by 54.
Problem 2
Can 810 be divided by 54 evenly?
Yes, 810 is divisible by 54.
Explanation
Let's verify using the divisibility rule:
1) Check divisibility by 2 and 27.
2) 810 is even, so it is divisible by 2.
3) For 27, sum the digits: 8 + 1 + 0 = 9, which isn't a multiple of 27. Check by division: 810 ÷ 54 = 15, which confirms it is divisible by 54 without a remainder.
Problem 3
Is 324 divisible by 54?
Yes, 324 is divisible by 54.
Explanation
To check divisibility:
1) Verify divisibility by 2 and 27.
2) 324 is even, so it is divisible by 2.
3) Sum the digits: 3 + 2 + 4 = 9, which isn't multiple of 27. Direct division shows 324 ÷ 54 = 6. Therefore, 324 is divisible by 54.
Problem 4
Check if 540 is divisible by 54.
Yes, 540 is divisible by 54.
Explanation
Check using the divisibility rule:
1) Verify divisibility by 2 and 27.
2) 540 is even, so it is divisible by 2.
3) Sum of digits: 5 + 4 + 0 = 9, which is not a multiple of 27, so check by division: 540 ÷ 54 = 10. Therefore, 540 is divisible by 54.
Problem 5
Determine if 1080 is divisible by 54.
Yes, 1080 is divisible by 54.
Explanation
Use the divisibility rule:
1) Check for 2 and 27.
2) 1080 is even, so divisible by 2.
3) Sum of digits: 1 + 0 + 8 + 0 = 9, not a multiple of 27. Verify by division: 1080 ÷ 54 = 20. Therefore, 1080 is divisible by 54.
FAQs on Divisibility Rule of 54
1.What is the divisibility rule for 54?
2.How many numbers are there between 1 and 200 that are divisible by 54?
3.Is 162 divisible by 54?
4.What if I get 0 after summing the digits?
5.Does the divisibility rule of 54 apply to all integers?
6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 54?
7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 54 with numbers?
8.What role do numbers and Divisibility Rule of 54 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 54 skills?
Important Glossaries for Divisibility Rule of 54
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number. For example, a number is divisible by 2 if it ends in an even number.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 54 are 54, 108, 162, etc.
- Integer: Whole numbers, including negative numbers and zero.
- Sum of digits: The total obtained by adding all the digits of a number.
- Even number: A number divisible by 2 without a remainder.
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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.
