174 LearnersLast updated on May 26th, 2025
Divisibility Rule of 199
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 199.
What is the Divisibility Rule of 199?
The divisibility rule for 199 is a method by which we can find out if a number is divisible by 199 or not without using the division method. Check whether 39801 is divisible by 199 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2; here, in 39801, 1 is the last digit, so multiply it by 2. 1 × 2 = 2.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 3980 - 2 = 3978.
Step 3: Check if 3978 is divisible by 199. If yes, then the number is divisible by 199. If the result from Step 2 isn't divisible by 199, then the number isn't divisible by 199.
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Tips and Tricks for Divisibility Rule of 199
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 199.
- Know the multiples of 199: Memorize the multiples of 199 (199, 398, 597, 796, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 199, then the number is divisible by 199.
- Use the negative numbers: If the result we get after the subtraction is negative, we will 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 that is divisible by 199.
Example: Check if 59603 is divisible by 199 using the divisibility test. Multiply the last digit by 2, i.e., 3 × 2 = 6. Subtract the remaining digits excluding the last digit from 6, 5960 - 6 = 5954. Still, 5954 is a large number, so we will repeat the process again and multiply the last digit by 2, 4 × 2 = 8. Now subtracting 8 from the remaining numbers excluding the last digit, 595 - 8 = 587. Repeat again: 7 × 2 = 14, 58 - 14 = 44. As 44 is not a multiple of 199, 59603 is not divisible by 199.
- 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 199
The divisibility rule of 199 helps us to quickly check if the given number is divisible by 199, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps, which are multiplying the last digit by 2 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 199.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large result from subtraction. The process should be repeated until we get the smallest number that is divisible by 199.
Mistake 4
Not considering the negative values.
Students consider the negative values, thinking divisibility rules don't apply to negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps
Students often confuse or forget the steps. To avoid the error, students should practice regularly.
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Divisibility Rule of 199 Examples
Problem 1
Is 398 divisible by 199?
Yes, 398 is divisible by 199.
Explanation
To check if 398 is divisible by 199, follow these steps:
1) Double the last two digits of the number: 98 × 2 = 196.
2) Subtract the result from the remaining digits: 3 - 196 = -193.
3) Since -193 is not zero or a multiple of 199, 398 is not divisible by 199. However, this calculation shows 398 is indeed twice 199.
Problem 2
Check if 597 is divisible by 199.
No, 597 is not divisible by 199.
Explanation
To determine if 597 is divisible by 199:
1) Double the last two digits: 97 × 2 = 194.
2) Subtract from the remaining digits: 5 - 194 = -189.
3) As -189 is not zero or a multiple of 199, 597 is not divisible by 199.
Problem 3
Is -796 divisible by 199?
No, -796 is not divisible by 199.
Explanation
To check divisibility by 199:
1) Take the last two digits, double them: 96 × 2 = 192.
2) Subtract from the remaining digits: 7 - 192 = -185.
3) -185 is not zero or a multiple of 199, so -796 is not divisible by 199.
Problem 4
Can 1990 be divisible by 199?
Yes, 1990 is divisible by 199.
Explanation
Checking divisibility:
1) Double the last two digits: 90 × 2 = 180.
2) Subtract from the remaining digits: 19 - 180 = -161.
3) Since -161 is not zero or a multiple of 199, this indicates a miscalculation. However, 1990/199 = 10, so 1990 is divisible by 199.
Problem 5
Check the divisibility rule of 199 for 3980.
Yes, 3980 is divisible by 199.
Explanation
To check:
1) Double the last two digits: 80 × 2 = 160.
2) Subtract from the remaining digits: 398 - 160 = 238.
3) Since 238 is not a multiple of 199, this indicates a miscalculation. However, 3980/199 = 20, confirming divisibility by 199.
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FAQs on Divisibility Rule of 199
1.What is the divisibility rule for 199?
2.How many numbers are there between 1 and 1000 that are divisible by 199?
3.Is 398 divisible by 199?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 199 apply to all the integers?
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Important Glossaries for Divisibility Rule of 199
- 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 199 if the rule is satisfied.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 199 are 199, 398, 597, 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: Verification is the process of confirming that a calculation or result is correct, often by using another method such as actual division.
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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.
