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147 LearnersLast updated on February 17th, 2025
Divisibility Rule of 729
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 729.
What is the Divisibility Rule of 729?
The divisibility rule for 729 is a method by which we can find out if a number is divisible by 729 or not without using the division method. Check whether 5832 is divisible by 729 with the divisibility rule.
Step 1: Break the number into groups of 3 digits from the right. For 5832, the groups are 5 and 832.
Step 2: Check if each group is divisible by 729. Since 832 is less than 729, check if 832 is divisible by 729 using the division method. If not, the whole number isn't divisible by 729.
Step 3: Since none of the groups is divisible by 729, 5832 is not divisible by 729.
Tips and Tricks for Divisibility Rule of 729
Learn the divisibility rule to help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 729.
Know the multiples of 729:
Memorize the multiples of 729 (729, 1458, 2187, etc.) to quickly check the divisibility. If the number is one of these multiples, it is divisible by 729.
Use the division method:
If the group is large and difficult to determine divisibility, use the division method for verification.
Repeat the process for large numbers:
If the number exceeds manageable size, break it into smaller groups of 3 digits and repeat the divisibility process for each group.
Practice with simple examples:
Start with smaller numbers to practice and understand the rule before applying it to large numbers.
Use technology for large calculations:
For very large numbers, using a calculator or computer can save time and reduce errors.
Common Mistakes and How to Avoid Them in Divisibility Rule of 729
The divisibility rule of 729 helps us to quickly check if the given number is divisible by 729, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not breaking the number into correct groups.
Ensure the number is properly divided into groups of 3 digits from the right.
Divisibility Rule of 729 Examples
Problem 1
Can 531441 be divided evenly by 729?
Yes, 531441 is divisible by 729.
Explanation
To determine if 531441 is divisible by 729, observe that 531441 is exactly 729 multiplied by 729 (i.e., 729²). Therefore, it is divisible by 729.
Problem 2
Is 262144 divisible by 729?
No, 262144 is not divisible by 729.
Explanation
First, consider that 729 is 3⁶. We can see that 262144 is a power of 2 (specifically 2¹⁸). Since 262144 is not a power of 3, it is not divisible by 729.
Problem 3
Check if 177147 is divisible by 729.
Yes, 177147 is divisible by 729.
Explanation
Notice that 177147 is a power of 3. Specifically, 177147 is 3¹¹, and since 729 is 3⁶, dividing 177147 by 729 gives us 3⁵, which is an integer.
Problem 4
Determine whether 500000 is divisible by 729.
No, 500000 is not divisible by 729.
Explanation
Since 500000 is not a power of 3, and 729 is, we can conclude that 500000 is not divisible by 729.
Problem 5
Is the number 729000 divisible by 729?
Yes, 729000 is divisible by 729.
Explanation
729000 can be expressed as 729 × 1000, which is a direct multiplication by 729, confirming that it is divisible by 729.
FAQs on Divisibility Rule of 729
1.What is the divisibility rule for 729?
2.How many numbers are there between 1 and 1000 that are divisible by 729?
3.Is 1458 divisible by 729?
4.What if I get 0 after dividing a group by 729?
5.Does the divisibility rule of 729 apply to all integers?
Important Glossary for Divisibility Rule of 729
- Divisibility rule: The set of rules used to determine whether a number is divisible by another number without performing division.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 729 are 729, 1458, 2187, etc.
- Integers: Whole numbers including positive, negative numbers, and zero.
- Division method: A mathematical operation to determine how many times one number is contained within another.
- Remainder: The amount left over when a number cannot be evenly divided by another.
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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.
