Table Of Contents
125 LearnersLast updated on February 18th, 2025
Divisibility Rule of 997
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 997
What is the Divisibility Rule of 997?
The divisibility rule for 997 is a method by which we can determine if a number is divisible by 997 without using the division method. Check whether 1994 is divisible by 997 with the divisibility rule.
Step 1: Multiply the last digit of the number by 3, here in 1994, 4 is the last digit, so multiply it by 3. 4 × 3 = 12
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 199–12 = 187.
Step 3: Since 187 is not a multiple of 997, repeat the process. Multiply the last digit of 187 by 3, which is 7 × 3 = 21.
Step 4: Subtract 21 from the remaining digits, 18–21 = -3. As 3 is not a multiple of 997, 1994 is not divisible by 997.
Tips and Tricks for Divisibility Rule of 997
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 997.
Know the multiples of 997:
Memorize the multiples of 997 (997, 1994, 2991, etc.) to quickly check the divisibility. If the result from subtraction is a multiple of 997, then the number is divisible by 997.
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 to determine divisibility by 997. For example, check if 3988 is divisible by 997 using the divisibility test. Multiply the last digit by 3, i.e., 8 × 3 = 24. Subtract the remaining digits excluding the last digit by 24, 398–24 = 374. Repeat the process: multiply the last digit by 3, 4 × 3 = 12. Now subtract 12 from the remaining numbers excluding the last digit, 37–12 = 25. Since 25 is not a multiple of 997, 3988 is not divisible by 997.
Use the division method to verify:
Students can use the division method as a way to verify and cross-check their results. This will help them verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 997
The divisibility rule of 997 helps us quickly check if the given number is divisible by 997, but common mistakes like calculation errors lead to incorrect results. Here we will understand some common mistakes that will help you to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps that involve multiplying the last digit with 3 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 997.
Divisibility Rule of 997 Examples
Problem 1
Is 1994 divisible by 997?
Yes, 1994 is divisible by 997.
Explanation
To check if 1994 is divisible by 997:
1) Divide the number directly by 997.
2) 1994 ÷ 997 = 2, remainder 0.
3) Since the remainder is 0, 1994 is divisible by 997.
Problem 2
Check the divisibility rule of 997 for 2985.
No, 2985 is not divisible by 997
Explanation
To check if 2985 is divisible by 997:
1) Divide the number directly by 997.
2) 2985 ÷ 997 = 2.994 (not an integer).
3) Since the result is not a whole number, 2985 is not divisible by 997.
Problem 3
Is -1994 divisible by 997?
Yes, -1994 is divisible by 997.
Explanation
To check if -1994 is divisible by 997:
1) Remove the negative sign and check divisibility for 1994.
2) 1994 ÷ 997 = 2, remainder 0.
3) Since the remainder is 0, -1994 is divisible by 997.
Problem 4
Can 3000 be divisible by 997 using the divisibility rule?
No, 3000 is not divisible by 997.
Explanation
To check if 3000 is divisible by 997:
1) Divide the number directly by 997.
2) 3000 ÷ 997 = 3.009 (not an integer).
3) Since the result is not a whole number, 3000 is not divisible by 997.
Problem 5
Check the divisibility rule of 997 for 996.
No, 996 is not divisible by 997.
Explanation
To check if 996 is divisible by 997:
1) Divide the number directly by 997.
2) 996 ÷ 997 = 0.998 (not an integer).
3) Since the result is not a whole number, 996 is not divisible by 997.
FAQs on Divisibility Rule of 997
1.What is the divisibility rule for 997?
2. How many numbers are there between 1 and 10,000 that are divisible by 997?
3.Is 2991 divisible by 997?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 997 apply to all integers?
Important Glossaries for Divisibility Rule of 997
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 997 are 997, 1994, 2991, etc.
- Integers: Integers are the numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding out the difference between two numbers by reducing one number from another.
- Verification: The process of confirming the correctness of a result or calculation.
Explore More numbers
Previous to Divisibility Rule of 997
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.
