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109 LearnersLast updated on February 18th, 2025
Divisibility Rule of 990
The divisibility rule is a way 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 990.
What is the Divisibility Rule of 990?
The divisibility rule for 990 is a method by which we can find out if a number is divisible by 990 or not without using the division method. Check whether 2970 is divisible by 990 with the divisibility rule.
Step 1: Check if the number is divisible by 2. Since 2970 is even, it is divisible by 2.
Step 2: Check if the number is divisible by 3. Add the digits of the number: 2 + 9 + 7 + 0 = 18, which is divisible by 3.
Step 3: Check if the number is divisible by 5. Since the last digit is 0, it is divisible by 5.
Step 4: Since 2970 is divisible by 2, 3, and 5, it is divisible by 990.
Tips and Tricks for Divisibility Rule of 990
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 990.
Know the prime factors of 990:
Memorize the prime factors of 990 (2, 3, 5, 11) to quickly check divisibility. Ensure the number is divisible by all these prime factors.
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.
Check divisibility in parts:
For large numbers, check divisibility by 2, then 3, then 5, and finally 11 to confirm divisibility by 990.
Common Mistakes and How to Avoid Them in Divisibility Rule of 990
The divisibility rule of 990 helps us to quickly check if a given number is divisible by 990, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you.
Mistake 1
Not checking all prime factors.
Ensure you check divisibility by 2, 3, 5, and 11, not just one or two of them.
Divisibility Rule of 990 Examples
Problem 1
Can a shipment of 5940 products be evenly divided into boxes of 990 products each?
Yes, 5940 is divisible by 990.
Explanation
To determine if 5940 can be divided evenly into boxes of 990, we need to check if 5940 is divisible by 990.
1) Check divisibility by 9: The sum of the digits of 5940 is 5 + 9 + 4 + 0 = 18, which is divisible by 9.
2) Check divisibility by 11: Alternating sum of the digits is (5 - 9 + 4 - 0) = 0, which is divisible by 11.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
Since 5940 is divisible by 9, 11, and 5, it is divisible by 990.
Problem 2
A batch of 2970 cookies needs to be packed in boxes of 990 cookies. Is this possible without leaving any cookies out?
Yes, 2970 is divisible by 990.
Explanation
To verify if 2970 can be packed into boxes of 990:
1) Check divisibility by 9: The sum of the digits of 2970 is 2 + 9 + 7 + 0 = 18, which is divisible by 9.
2) Check divisibility by 11: Alternating sum of the digits is (2 - 9 + 7 - 0) = 0, which is divisible by 11.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
Since 2970 is divisible by 9, 11, and 5, it is divisible by 990.
Problem 3
Is a payment of 7920 dollars divisible into 8 installments of 990 dollars each?
Yes, 7920 is divisible by 990.
Explanation
To check if 7920 can be divided into 8 installments of 990:
1) Check divisibility by 9: The sum of the digits of 7920 is 7 + 9 + 2 + 0 = 18, which is divisible by 9.
2) Check divisibility by 11: Alternating sum of the digits is (7 - 9 + 2 - 0) = 0, which is divisible by 11.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
Since 7920 is divisible by 9, 11, and 5, it is divisible by 990.
Problem 4
A company needs to distribute 4550 flyers evenly using packets of 990 each. Can this be done without any flyers left over?
No, 4550 is not divisible by 990.
Explanation
To determine if 4550 can be evenly distributed:
1) Check divisibility by 9: The sum of the digits of 4550 is 4 + 5 + 5 + 0 = 14, which is not divisible by 9.
Since 4550 is not divisible by 9, it is not divisible by 990.
Problem 5
A theater wants to sell 8910 tickets in batches of 990. Is this possible?
Yes, 8910 is divisible by 990.
Explanation
To verify if 8910 can be sold in batches of 990:
1) Check divisibility by 9: The sum of the digits of 8910 is 8 + 9 + 1 + 0 = 18, which is divisible by 9.
2) Check divisibility by 11: Alternating sum of the digits is (8 - 9 + 1 - 0) = 0, which is divisible by 11.
3) Check divisibility by 5: The last digit is 0, which is divisible by 5.
Since 8910 is divisible by 9, 11, and 5, it is divisible by 990.
FAQs on Divisibility Rule of 990
1.What is the divisibility rule for 990?
2.How many numbers are there between 1 and 1000 that are divisible by 990?
3. Is 1980 divisible by 990?
4.What if I get 0 after checking all factors?
5. Does the divisibility rule of 990 apply to all integers?
Important Glossaries for Divisibility Rule of 990
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Prime factors: The prime numbers that multiply together to give a specific number, such as 2, 3, 5, and 11 for 990.
- Multiple: A number that can be divided by another number without a remainder.
- Even number: A number divisible by 2.
- Sum of digits: The total obtained by adding all the digits of a number, used to check divisibility by 3.
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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.
