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119 LearnersLast updated on February 18th, 2025
Divisibility Rule of 882
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 882.
What is the Divisibility Rule of 882?
The divisibility rule for 882 is a method by which we can determine if a number is divisible by 882 without using the division method.
Check whether 1764 is divisible by 882 using the divisibility rule.
Step 1: Verify divisibility by 2: The number must be even. Here, 1764 is even, so it passes this step.
Step 2: Verify divisibility by 3: Add the digits of the number. If the sum is divisible by 3, then the number is divisible by 3. Here, 1 + 7 + 6 + 4 = 18, and 18 is divisible by 3.
Step 3: Verify divisibility by 7: Follow the rule for 7 (multiply the last digit by 2 and subtract from the rest). Here, 4 × 2 = 8, and 176 - 8 = 168. Since 168 is divisible by 7, 1764 is also divisible by 7.
Step 4: If a number is divisible by 2, 3, and 7, it is divisible by 882. Therefore, 1764 is divisible by 882.
Tips and Tricks for Divisibility Rule of 882
Learning the divisibility rule will help you master division. Let’s explore a few tips and tricks for the divisibility rule of 882.
Know the factors of 882:
Memorize the factors of 882 (2, 3, 7) to quickly check divisibility. A number divisible by all these factors is divisible by 882.
Use negative numbers:
If the result after subtraction in the rule for 7 is negative, consider it as positive for checking divisibility.
Repeat the process for large numbers:
Keep repeating the divisibility checks for 2, 3, and 7 until you reach smaller numbers.
Use the division method to verify:
Use division to verify and cross-check your results for accuracy.
Common Mistakes and How to Avoid Them in Divisibility Rule of 882
The divisibility rule of 882 helps us quickly check if a number is divisible by 882, but errors can lead to incorrect conclusions. Here we will understand some common mistakes and how to avoid them.
Mistake 1
Not checking all factors (2, 3, and 7).
Ensure you check divisibility by 2, 3, and 7. Only then can you conclude divisibility by 882.
Divisibility Rule of 882 Examples
Problem 1
Is 2646 divisible by 882?
Yes, 2646 is divisible by 882.
Explanation
To determine if 2646 is divisible by 882, we can break down the divisibility rules for the factors of 882, which are 2, 3, and 7.
1) Divisibility by 2: The number is even, so it is divisible by 2.
2) Divisibility by 3: Sum the digits, 2 + 6 + 4 + 6 = 18, which is divisible by 3.
3) Divisibility by 7: Double the last digit and subtract from the rest, 264 - 12 = 252, then 25 - 4 = 21, which is divisible by 7.
Since 2646 satisfies divisibility rules for 2, 3, and 7, it is divisible by 882.
Problem 2
Check the divisibility rule of 882 for 1764.
Yes, 1764 is divisible by 882.
Explanation
To check if 1764 is divisible by 882, we must verify divisibility by 2, 3, and 7.
1) Divisibility by 2: The number ends in 4, an even number.
2) Divisibility by 3: Sum the digits, 1 + 7 + 6 + 4 = 18, which is divisible by 3.
3) Divisibility by 7: Double the last digit and subtract from the rest, 176 - 8 = 168, then 16 - 16 = 0, confirming divisibility by 7.
1764 meets all criteria, therefore it is divisible by 882.
Problem 3
Is -3528 divisible by 882?
Yes, -3528 is divisible by 882.
Explanation
We first consider the absolute value and check divisibility by 2, 3, and 7.
1) Divisibility by 2: The last digit, 8, is even.
2) Divisibility by 3: Sum the digits, 3 + 5 + 2 + 8 = 18, which is divisible by 3.
3) Divisibility by 7: Double the last digit and subtract from the rest, 352 - 16 = 336, then 33 - 12 = 21, which is divisible by 7.
Thus, -3528 is divisible by 882.
Problem 4
Can 1234 be divisible by 882 following the divisibility rule?
No, 1234 is not divisible by 882.
Explanation
We check the divisibility by 2, 3, and 7.
1) Divisibility by 2: The number ends in 4, so it is even.
2) Divisibility by 3: Sum the digits, 1 + 2 + 3 + 4 = 10, which is not divisible by 3.
3) Divisibility by 7: Double the last digit and subtract from the rest, 123 - 8 = 115, which is not divisible by 7.
Since 1234 does not meet all criteria, it is not divisible by 882.
Problem 5
Check the divisibility rule of 882 for 5292.
Yes, 5292 is divisible by 882.
Explanation
Confirm divisibility by 2, 3, and 7.
1) Divisibility by 2: The number ends in 2, an even number.
2) Divisibility by 3: Sum the digits, 5 + 2 + 9 + 2 = 18, which is divisible by 3.
3) Divisibility by 7: Double the last digit and subtract from the rest, 529 - 4 = 525, then 52 - 10 = 42, which is divisible by 7.
5292 meets all criteria, confirming divisibility by 882.
FAQs on Divisibility Rule of 882
1.What is the divisibility rule for 882?
2.How many numbers between 1 and 10000 are divisible by 882?
3.Is 2646 divisible by 882?
4.What if I get 0 after any operation?
5.Does the divisibility rule of 882 apply to all integers?
Important Glossary for Divisibility Rule of 882
- Divisibility rule: A set of guidelines used to determine if a number is divisible by another number without performing division.
- Factors: Numbers that divide another number completely without leaving a remainder.
- Multiple: The product of a number and an integer.
- Integer: A whole number that can be positive, negative, or zero.
- Subtraction: The process of finding the difference between two numbers.
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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.
