188 LearnersLast updated on May 26th, 2025
Divisibility Rule of 171
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 171.
What is the Divisibility Rule of 171?
The divisibility rule for 171 is a method by which we can find out if a number is divisible by 171 or not without using the division method. Check whether 3420 is divisible by 171 with the divisibility rule.
Step 1: Check if the number is divisible by both 9 and 19, because the prime factorization of 171 is 9 × 19.
To check divisibility by 9, sum the digits of the number. If the sum is a multiple of 9, then the number is divisible by 9. For 3420, the sum of the digits is 3+4+2+0=9, which is a multiple of 9.
To check divisibility by 19, use the divisibility rule for 19: Multiply the last digit by 2, subtract this from the remaining leading truncated number, and check if the result is a multiple of 19. For 3420, multiply 0 by 2, which is 0. Subtract 0 from 342, so 342. Now, 342 ÷ 19 = 18, which is a whole number, so it is divisible by 19.
Step 2: Since 3420 is divisible by both 9 and 19, it is also divisible by 171.
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Tips and Tricks for the Divisibility Rule of 171
Knowing the divisibility rules for 9 and 19 will help you master the rule for 171.
- Know the multiples of 171: Memorize the multiples of 171 (171, 342, 513, 684, etc.) to quickly check divisibility.
- Use the sum of digits: Quickly check if the sum of the digits is divisible by 9.
- Repeat the process for large numbers: If the number is large, you can break down the checks to ensure accuracy.
For example, check if 6849 is divisible by 171. First, check for divisibility by 9: 6+8+4+9=27, which is divisible by 9.
Then, for divisibility by 19: Multiply the last digit by 2 (9×2=18), subtract from the truncated number (684-18=666), and check if 666 is divisible by 19.
Since 666 ÷ 19 = 35.05, it is not divisible, thus 6849 is not divisible by 171.
- Use the division method to verify: Verify results by dividing the number by 171 to confirm your result.
Common Mistakes and How to Avoid Them in the Divisibility Rule of 171
The divisibility rule of 171 helps us to quickly check if a given number is divisible by 171, but common mistakes like calculation errors lead to incorrect conclusions. Here are some common mistakes to avoid:
Mistake 1
Not checking both 9 and 19.
Ensure you check divisibility by both 9 and 19.
Mistake 2
Incorrectly summing the digits or applying the wrong rule for 19.
Double-check the summation and carefully apply the rule for 19.
Mistake 3
Not considering the whole number.
Ensure the entire number is considered when checking divisibility.
Mistake 4
Confusing the steps for 9 and 19.
Practice the steps separately to reinforce understanding.
Mistake 5
Forgetting to verify with division.
Always verify with actual division if unsure.
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Divisibility Rule of 171 Examples
Problem 1
Is 1197 divisible by 171?
No, 1197 is not divisible by 171.
Explanation
To check if 1197 is divisible by 171, use the following steps:
1) Consider the last three digits as a separate number: 197.
2) Subtract this three-digit number from the number formed by the rest of the digits: 1 - 197 = -196.
3) Check if -196 is divisible by 171. Since it is not, 1197 is not divisible by 171.
Problem 2
Can 2052 be divisible by 171 using the divisibility rule?
Yes, 2052 is divisible by 171.
Explanation
To determine if 2052 is divisible by 171, proceed as follows:
1) Consider the last three digits as a separate number: 052.
2) Subtract this three-digit number from the number formed by the rest of the digits: 20 - 52 = -32.
3) Check if -32 is divisible by 171. Since -32 is not a multiple of 171, let's try another method by dividing 2052 directly by 171 to see if it results in a whole number: 2052 ÷ 171 = 12, a whole number, hence 2052 is divisible by 171.
Problem 3
Determine the divisibility of 3429 by 171.
Yes, 3429 is divisible by 171.
Explanation
Check divisibility of 3429 by 171:
1) Consider the last three digits as a separate number: 429.
2) Subtract this three-digit number from the number formed by the rest of the digits: 3 - 429 = -426.
3) Since -426 is not a multiple of 171, divide 3429 directly by 171 to verify: 3429 ÷ 171 = 20.05. Since it is not a whole number, 3429 is actually not divisible by 171. (Upon re-evaluation, this was an error in calculation, showing the importance of double-checking results.)
Problem 4
Is 684 divisible by 171 using the divisibility rule?
Yes, 684 is divisible by 171.
Explanation
To verify if 684 is divisible by 171, apply the steps:
1) Consider the last three digits as a separate number: 684.
2) Subtract this three-digit number from the number formed by the rest of the digits: 0 - 684 = -684.
3) Check if -684 is divisible by 171. Since -684 ÷ 171 = -4, a whole number, 684 is divisible by 171.
Problem 5
Verify the divisibility of 513 by 171.
No, 513 is not divisible by 171.
Explanation
To check if 513 is divisible by 171, use these steps:
1) Consider the last three digits as a separate number: 513.
2) Subtract this three-digit number from the number formed by the rest of the digits: 0 - 513 = -513.
3) Since -513 ÷ 171 does not yield a whole number (it equals -3), 513 is not divisible by 171.
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FAQs on Divisibility Rule of 171
1.What is the divisibility rule for 171?
2.How many numbers are there between 1 and 1000 that are divisible by 171?
3.Is 513 divisible by 171?
4.What if I get 0 after using the rule for 19?
5.Does the divisibility rule of 171 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 171?
7.What are some fun ways kids in India can practice Divisibility Rule of 171 with numbers?
8.What role do numbers and Divisibility Rule of 171 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Divisibility Rule of 171 skills?
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Important Glossaries for Divisibility Rule of 171
- Divisibility Rule: A set of guidelines to determine if a number is divisible by another without performing division.
- Multiple: A number that can be divided by another number without leaving a remainder.
- Sum of Digits: The total obtained by adding all the digits of a number.
- Prime Factorization: Breaking down a number into its basic building blocks, or prime numbers.
- Integer: A whole number, positive or negative, including zero.
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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.
