182 LearnersLast updated on May 26th, 2025
Divisibility Rule of 829
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 829.
What is the Divisibility Rule of 829?
The divisibility rule for 829 is a method by which we can find out if a number is divisible by 829 or not without using the division method. Check whether 12435 is divisible by 829 with the divisibility rule.
Step 1: Multiply the last digit of the number by a specific factor (let's say, 9). Here in 12435, 5 is the last digit, multiply it by 9. 5 × 9 = 45.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. That is, 1243 - 45 = 1198.
Step 3: Repeat the process with 1198. Multiply the last digit (8) by 9. 8 × 9 = 72.
Step 4: Subtract 72 from 119. 119 - 72 = 47.
Step 5: Since 47 is not zero or divisible by 829, 12435 is not divisible by 829.
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Tips and Tricks for Divisibility Rule of 829
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 829.
Know the multiples of 829:
Memorize the multiples of 829 (e.g., 829, 1658, 2487, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 829, then the number is divisible by 829.
Use the negative numbers:
If the result we get after subtraction is negative, we will avoid the symbol and consider it as positive for checking the divisibility of a number.
Repeat the process for large numbers:
Students should keep repeating the divisibility process until they reach a small number that is clearly divisible by 829.
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 829
The divisibility rule of 829 helps us to quickly check if the given number is divisible by 829, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that are multiplying the last digit with the specific factor (e.g., 9) and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 829.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have got a large number resulting from the subtraction. The process should be repeated until we get the smallest number that is divisible by 829.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to the negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget the steps. To avoid the error, students should practice regularly.
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Divisibility Rule of 829 Examples
Problem 1
Is 4974 divisible by 829?
Yes, 4974 is divisible by 829.
Explanation
To check if 4974 is divisible by 829, use a hypothetical divisibility rule for 829:
1) Multiply the last three digits of the number by 3, 974 × 3 = 2922.
2) Subtract the result from the remaining digits, excluding the last three digits. Here, the remaining digits are 4, so 4 - 2922 = -2918.
3) Check if the result is a multiple of 829. Yes, -2918 divided by 829 equals -3.52, indicating a multiple (with absolute value considered).
Problem 2
Check the divisibility rule of 829 for 1658.
No, 1658 is not divisible by 829.
Explanation
For checking the divisibility rule of 829 for 1658:
1) Multiply the last three digits by 3, 658 × 3 = 1974.
2) Subtract the result from the remaining digits, excluding the last three digits. Here, the remaining digit is 1, so 1 - 1974 = -1973.
3) Check if the result is a multiple of 829. No, -1973 divided by 829 is not an integer, thus not divisible.
Problem 3
Is 2487 divisible by 829?
No, 2487 is not divisible by 829.
Explanation
To check if 2487 is divisible by 829:
1) Multiply the last three digits by 3, 487 × 3 = 1461.
2) Subtract the result from the remaining digit, excluding the last three digits. Here, the remaining digit is 2, so 2 - 1461 = -1459.
3) Check if the result is a multiple of 829. No, -1459 divided by 829 is not an integer, hence not divisible.
Problem 4
Can 6629 be divisible by 829 following the divisibility rule?
Yes, 6629 is divisible by 829.
Explanation
To check if 6629 is divisible by 829:
1) Multiply the last three digits by 3, 629 × 3 = 1887.
2) Subtract the result from the remaining digit, excluding the last three digits. Here, the remaining digit is 6, so 6 - 1887 = -1881.
3) Check if the result is a multiple of 829. Yes, -1881 divided by 829 equals -2.27, indicating a multiple (with absolute value considered).
Problem 5
Check the divisibility rule of 829 for 8290.
Yes, 8290 is divisible by 829.
Explanation
To check the divisibility rule of 829 for 8290:
1) Multiply the last three digits by 3, 290 × 3 = 870.
2) Subtract the result from the remaining digits, excluding the last three digits. Here, the remaining digit is 8, so 8 - 870 = -862.
3) Check if the result is a multiple of 829. Yes, -862 divided by 829 equals approximately -1.04, indicating a multiple (with absolute value considered).
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FAQs on Divisibility Rule of 829
1.What is the divisibility rule for 829?
2.How many numbers are there between 1 and 10000 that are divisible by 829?
3.Is 3316 divisible by 829?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 829 apply to all integers?
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Important Glossaries for Divisibility Rule of 829
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not. For example, a number is divisible by 2 if the number ends with an even number.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 829 are 829, 1658, 2487, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers, by reducing one number from another.
- Verification: The process of checking the accuracy or validity of a calculation, often using an alternative method like division.
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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.
