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116 LearnersLast updated on February 18th, 2025
Divisibility Rule of 991
The divisibility rule is a technique to determine if a number is divisible by another number without performing the actual division. In real life, we can use divisibility rules for quick math, dividing things evenly, and sorting items. In this topic, we will learn about the divisibility rule of 991.
What is the Divisibility Rule of 991?
The divisibility rule for 991 is a method to find out if a number is divisible by 991 without performing the division directly. Let's check whether 108,901 is divisible by 991 using the divisibility rule.
Step 1: Separate the last three digits of the number. In 108,901, 901 is the last three digits.
Step 2: Subtract 901 from the remaining part of the number, which is 108. 108 - 901 = -793.
Step 3: Check if the result from Step 2 is divisible by 991. In this case, -793 is not divisible by 991. Therefore, 108,901 is not divisible by 991. If the result is divisible by 991, then the number is divisible by 991.
Tips and Tricks for Divisibility Rule of 991
Understanding the divisibility rule will help in mastering division. Let’s learn a few tips and tricks for the divisibility rule of 991.
Know the multiples of 991:
Memorize the multiples of 991 (991, 1982, 2973, etc.) to quickly check divisibility. If the result from subtraction is a multiple of 991, the number is divisible by 991.
Use negative numbers:
If the result after subtraction is negative, consider the absolute value for checking divisibility.
Repeat the process for large numbers:
Continue the divisibility process until reaching a small number that is easily checked against 991. For example, check if 297,991 is divisible by 991. Separate the last three digits (991) and subtract from the remaining number (297), giving 297 - 991 = -694. Since -694 is not divisible by 991, neither is 297,991.
Use the division method to verify:
Verify results using the division method to ensure accuracy and understanding.
Common Mistakes and How to Avoid Them in Divisibility Rule of 991
The divisibility rule of 991 helps quickly determine if a number is divisible by 991, but errors can lead to incorrect results. Here are some common mistakes and how to avoid them.
Mistake 1
Not following correct steps.
Follow the correct steps: separate the last three digits and subtract from the remaining number.
Divisibility Rule of 991 Examples
Problem 1
Is 3964 divisible by 991?
No, 3964 is not divisible by 991.
Explanation
To check if 3964 is divisible by 991, apply the divisibility rule
1) Take the last three digits of the number, which are 964.
2) Subtract the result from the remaining leading digits: 3 - 964.
3) The result is negative, and it does not simplify to a multiple of 991, so 3964 is not divisible by 991.
Problem 2
Can 1982 be divisible by 991 following the divisibility rule?
Yes, 1982 is divisible by 991.
Explanation
To verify if 1982 is divisible by 991:
1) Take the last three digits, which are 982.
2) Subtract these from the remaining leading digits: 1 - 982 results in -981.
3) The absolute value of -981 is close to 991, but it does not simplify to a multiple of 991. However, since the subtraction results in a remainder close to 0, this confirms 1982 is divisible by 991.
Problem 3
Is 991 divisible by 991?
Yes, 991 is divisible by 991.
Explanation
Any number is divisible by itself. For 991:
1) The last three digits are 991.
2) Subtract from the leading digits (which are 0): 0 - 991 = -991.
3) -991 is a multiple of 991, confirming divisibility.
Problem 4
Check the divisibility rule of 991 for 2973.
Yes, 2973 is divisible by 991.
Explanation
To check if 2973 follows the divisibility rule:
1) Take the last three digits, which are 973.
2) Subtract from the remaining leading digit: 2 - 973 = -971.
3) The negative result simplifies to a multiple of 991, thus confirming 2973 is divisible by 991.
Problem 5
Is 5000 divisible by 991?
No, 5000 is not divisible by 991.
Explanation
To test if 5000 is divisible by 991:
1) Take the last three digits, which are 000.
2) Subtract from the leading digit: 5 - 0 = 5.
3) The result, 5, is not a multiple of 991, so 5000 is not divisible by 991.
FAQs on Divisibility Rule of 991
1.What is the divisibility rule for 991?
2.How many numbers are there between 1 and 10,000 that are divisible by 991?
3. Is 1982 divisible by 991?
4. What if I get 0 after subtracting?
5. Does the divisibility rule of 991 apply to all integers?
Important Glossaries for Divisibility Rule of 991
- Divisibility rule: A set of guidelines used to determine if one number is divisible by another without direct division.
- Multiples: Results obtained by multiplying a number by an integer. For example, multiples of 991 are 991, 1982, 2973, etc.
- Integers: Numbers including all whole numbers, negative numbers, and zero.
- Subtraction: The process of finding the difference between two numbers by deducting one from the other.
- Negative numbers: Numbers less than zero, used in calculations by considering their absolute values when checking divisibility.
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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.
