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133 LearnersLast updated on February 17th, 2025
Divisibility Rule of 827
The divisibility rule is a way to determine if 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 827.
What is the Divisibility Rule of 827?
The divisibility rule for 827 is a method by which we can find out if a number is divisible by 827 or not without using the division method. Check whether 2481 is divisible by 827 with the divisibility rule.
Step 1: Multiply the last digit of the number by 3, here in 2481, 1 is the last digit. Multiply it by 3. 1 × 3 = 3
Step 2: Subtract the result from Step 1 with the remaining values but do not include the last digit, i.e., 248–3 = 245.
Step 3: As it is shown that 245 is not a multiple of 827, therefore, the number is not divisible by 827. If the result from step 2 was a multiple of 827, then the number would be divisible by 827.
Tips and Tricks for Divisibility Rule of 827
Learning divisibility rules will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 827.
Know the multiples of 827:
Memorize the multiples of 827 (827, 1654, 2481, 3308…etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 827, then the number is divisible by 827.
Use the negative numbers:
If the result we get after the 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 divisible by 827. For example: Check if 4962 is divisible by 827 using the divisibility test. Multiply the last digit by 3, i.e., 2 × 3 = 6. Subtract the remaining digits excluding the last digit by 6, 496–6 = 490. Still, 490 is a large number, hence we will repeat the process again and multiply the last digit by 3, 0 × 3 = 0. Now, subtracting 0 from the remaining numbers excluding the last digit, 49–0 = 49. As 49 is not a multiple of 827, 4962 is not divisible by 827.
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 827
The divisibility rule of 827 helps us quickly check if a given number is divisible by 827, but common mistakes like calculation errors lead to incorrect results. 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: multiplying the last digit by 3 and then subtracting the result from the remaining digits excluding the last digit and checking if it is a multiple of 827
Divisibility Rule of 827 Examples
Problem 1
Is 2481 divisible by 827?
Yes, 2481 is divisible by 827.
Explanation
To check divisibility by 827, we look for a pattern or rule specific to 827.
1) Divide the number by 827 directly to see if it results in a whole number.
2481 ÷ 827 = 3.
2) Since the result is a whole number, 2481 is divisible by 827.
Problem 2
Check the divisibility of 827 for 66216.
Yes, 66216 is divisible by 827.
Explanation
To verify divisibility, we can use division.
1) Divide 66216 by 827.
66216 ÷ 827 = 80.
2) Since the result is a whole number, 66216 is divisible by 827.
Problem 3
Is 1654 divisible by 827?
No, 1654 is not divisible by 827.
Explanation
To check divisibility, divide the number by 827.
1) Perform the division of 1654 by 827.
1654 ÷ 827 = 2 (remainder 0).
2) Since there is no remainder, 1654 is divisible by 827.
Problem 4
Can 331 be divisible by 827 following any divisibility rule?
No, 331 is not divisible by 827.
Explanation
331 is less than 827, so it cannot be divisible by 827.
1) Check by attempting division:
331 ÷ 827 = 0.4 (not a whole number).
2) Since the result is not a whole number, 331 is not divisible by 827.
Problem 5
Check the divisibility rule of 827 for 8270.
Yes, 8270 is divisible by 827.
Explanation
To check divisibility, divide 8270 by 827.
1) Perform the division:
8270 ÷ 827 = 10.
2) Since the result is a whole number, 8270 is divisible by 827.
FAQs on Divisibility Rule of 827
1.What is the divisibility rule for 827?
2.How many numbers are there between 1 and 10000 that are divisible by 827
3.Is 3308 divisible by 827?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 827 apply to all integers?
Important Glossaries for Divisibility Rule of 827
- 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 even numbers.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example: multiples of 827 are 827, 1654, 2481, 3308, etc.
- Integers: Integers are numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding out the difference between two numbers by reducing one number from another.
- Verification: The process of using another method, such as division, to confirm the results obtained from the divisibility rule.
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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.
