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136 LearnersLast updated on February 18th, 2025
Divisibility Rule of 880
The divisibility rule is a method to determine 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 880.
What is the Divisibility Rule of 880?
The divisibility rule for 880 is a method by which we can find out if a number is divisible by 880 or not without using the division method.
Tips and Tricks for Divisibility Rule of 880
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 880.
Know the multiples of 880:
Memorize the multiples of 880 (880, 1760, 2640, 3520, etc.) to quickly check divisibility. If the result of the calculation is a multiple of 880, then the number is divisible by 880.
Understand the divisibility rules for 8 and 11:
Since 880 is 8×110, a number divisible by 880 must be divisible by both 8 and 11. A number is divisible by 8 if its last three digits form a number divisible by 8. A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11.
Check using smaller divisors:
For large numbers, check divisibility by 8 and 11 separately. For example, to check if 7040 is divisible by 880, first check divisibility by 8 and 11. Since 040 (40) is divisible by 8 and the alternating sum for 7040 is (7+0)-(0+4)=3, which is not a multiple of 11, 7040 is not divisible by 880.
Use the division method to verify:
You can use the division method to verify and cross-check your results, helping to confirm and learn the divisibility rule.
Common Mistakes and How to Avoid Them in Divisibility Rule of 880
The divisibility rule of 880 helps us quickly check if a number is divisible by 880, but common mistakes like calculation errors can lead to incorrect conclusions. Here are some common mistakes and tips to avoid them:
Mistake 1
Not checking divisibility by both 8 and 11.
Ensure to check divisibility using both rules, as a number must satisfy both to be divisible by 880.
Divisibility Rule of 880 Examples
Problem 1
Is 3520 divisible by 880?
No, 3520 is not divisible by 880.
Explanation
To check if 3520 is divisible by 880, we need to ensure it meets the divisibility rules for 8, 11, and 10 (since 880 = 8 × 11 × 10).
1) Divisibility by 8: The last three digits are 520, which is not divisible by 8.
2) Divisibility by 11: The difference between the sum of digits in odd positions (3 + 2) and even positions (5 + 0) is 0, which is divisible by 11.
3) Divisibility by 10: The last digit is 0, so it's divisible by 10.
Since 520 is not divisible by 8, 3520 is not divisible by 880.
Problem 2
Check if 8800 is divisible by 880.
Yes, 8800 is divisible by 880.
Explanation
To verify the divisibility of 8800 by 880, we check divisibility by 8, 11, and 10:
1) Divisibility by 8: The last three digits are 800, which is divisible by 8 (800 ÷ 8 = 100).
2) Divisibility by 11: The difference between the sum of digits in odd positions (8 + 0) and even positions (8 + 0) is 0, which is divisible by 11.
3) Divisibility by 10: The last digit is 0, so it's divisible by 10.
All conditions are satisfied, so 8800 is divisible by 880.
Problem 3
Is -1760 divisible by 880?
Yes, -1760 is divisible by 880.
Explanation
We check the divisibility of 1760 (ignoring the negative sign) by 880:
1) Divisibility by 8: The last three digits are 760, which is divisible by 8 (760 ÷ 8 = 95).
2) Divisibility by 11: The difference between the sum of digits in odd positions (1 + 6) and even positions (7 + 0) is 0, which is divisible by 11.
3) Divisibility by 10: The last digit is 0, so it's divisible by 10.
Since all conditions are met, -1760 is divisible by 880.
Problem 4
Can 440 be divisible by 880 following the divisibility rule?
No, 440 is not divisible by 880.
Explanation
To check if 440 is divisible by 880, we need to verify its divisibility by 8, 11, and 10:
1) Divisibility by 8: The last three digits are 440, which is not divisible by 8.
2) Divisibility by 11: The difference between the sum of digits in odd positions (4 + 0) and even positions (4) is 0, which is divisible by 11.
3) Divisibility by 10: The last digit is 0, so it's divisible by 10.
Since 440 is not divisible by 8, it is not divisible by 880.
Problem 5
Check the divisibility rule of 880 for 9680.
Yes, 9680 is divisible by 880.
Explanation
For divisibility of 9680 by 880, we verify divisibility by 8, 11, and 10:
1) Divisibility by 8: The last three digits are 680, which is divisible by 8 (680 ÷ 8 = 85).
2) Divisibility by 11: The difference between the sum of digits in odd positions (9 + 8) and even positions (6 + 0) is 11, which is divisible by 11.
3) Divisibility by 10: The last digit is 0, so it's divisible by 10.
All conditions are satisfied, so 9680 is divisible by 880.
FAQs on Divisibility Rule of 880
1.What is the divisibility rule for 880?
2.How many numbers are there between 1 and 10000 that are divisible by 880?
3.Is 3520 divisible by 880?
4.What if I get 0 after checking divisibility?
5.Does the divisibility rule of 880 apply to all integers?
Important Glossaries for Divisibility Rule of 880
- 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 880 if it meets the criteria of divisibility by both 8 and 11.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 880 are 880, 1760, 2640, etc.
- Integers: Integers are the 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.
- Alternating sum: The process of adding and subtracting digits in alternating positions to check divisibility by 11.
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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.
