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133 LearnersLast updated on February 12th, 2025
Divisibility Rule of 324
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 324.
What is the Divisibility Rule of 324?
The divisibility rule for 324 is a method by which we can determine if a number is divisible by 324 without using the division method. Check whether 648 is divisible by 324 using the divisibility rule.
Step 1: Check if the number is divisible by 4. For 648, the last two digits are 48, and 48 is divisible by 4.
Step 2: Check if the number is divisible by 81. Sum the digits of 648: 6 + 4 + 8 = 18. Since 18 is not divisible by 81, 648 is not divisible by 324.
Tips and Tricks for Divisibility Rule of 324
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 324.
- Know the factors of 324: Memorize the factors of 324 (2^2, 3^4) to quickly check divisibility. A number must be divisible by both 4 and 81 to be divisible by 324.
- Use smaller tests: If the number is too large, break it down by testing smaller parts separately for divisibility by 4 and 81.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 324. For example: Check if 1296 is divisible by 324 using the divisibility test. Verify divisibility by 4 and 81 separately.
- Use the division method to verify: Students can use the division method as a way to verify and cross-check their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 324
The divisibility rule of 324 helps us quickly check if a given number is divisible by 324, but common mistakes like calculation errors lead to incorrect conclusions. Here we will understand some common mistakes that will help you understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps of checking divisibility by 4 and 81 separately.
Divisibility Rule of 324 Examples
Problem 1
Is 1296 divisible by 324?
Yes, 1296 is divisible by 324.
Explanation
To check if 1296 is divisible by 324, break down the number into its prime factors:
1) 1296 = 24 × 34.
2) 324 = 22 × 34.
3) Since 1296 has the same or more powers of 2 and 3 as 324, 1296 is divisible by 324.
Problem 2
Check the divisibility rule of 324 for 648.
Yes, 648 is divisible by 324.
Explanation
To determine if 648 is divisible by 324, we factor the numbers:
1) 648 = 23 × 34.
2) 324 = 22 × 34.
3) The power of 2 in 648 is greater than in 324, and the powers of 3 are equal, so 648 is divisible by 324.
Problem 3
Is 972 divisible by 324?
Yes, 972 is divisible by 324.
Explanation
We check the prime factorization:
1) 972 = 22 × 35.
2) 324 = 22 × 34.
3) Since 972 has the required powers of 2 and more powers of 3, it is divisible by 324.
Problem 4
Can 108 be divisible by 324 following the divisibility rule?
No, 108 is not divisible by 324.
Explanation
Check the factors:
1) 108 = 22 × 33.
2) 324 = 22 × 34.
3) 108 lacks enough factors of 3 to be divisible by 324.
Problem 5
Check the divisibility rule of 324 for 2592.
Yes, 2592 is divisible by 324.
Explanation
Factor both numbers:
1) 2592 = 25 × 34.
2) 324 = 22 × 34.
3) 2592 has equal or greater factors of 2 and 3 compared to 324, so it is divisible by 324.
FAQs on Divisibility Rule of 324
1.What is the divisibility rule for 324?
2.How many numbers are there between 1 and 1000 that are divisible by 324?
3.Is 972 divisible by 324?
4.What if I get a remainder after checking divisibility by 81?
5.Does the divisibility rule of 324 apply to all integers?
Important Glossaries for Divisibility Rule of 324
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number without performing division.
- Factors: Numbers that divide another number exactly without leaving a remainder. Example: Factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
- Multiple: A number that can be divided by another number without leaving a remainder. For example, 648 is a multiple of 324.
- Sum of digits: The sum obtained by adding all the digits of a number. Used to check divisibility by 9 and 81.
- Subtraction: The process of finding the difference between two numbers, not typically used directly in the divisibility rule for 324 but relevant in number operations.
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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.
