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Last updated on February 17th, 2025

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Divisibility Rule of 171

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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.

Divisibility Rule of 171 for US Students
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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.

 

divisibility rule of 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.
     
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Common Mistakes and How to Avoid Them in the Divisibility Rule of 171

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Divisibility Rule of 171 Examples

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Problem 1

Is 1197 divisible by 171?

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Explanation

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Problem 2

Can 2052 be divisible by 171 using the divisibility rule?

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Explanation

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Problem 3

Determine the divisibility of 3429 by 171.

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Explanation

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Problem 4

Is 684 divisible by 171 using the divisibility rule?

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Explanation

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Problem 5

Verify the divisibility of 513 by 171.

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Explanation

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FAQs on Divisibility Rule of 171

1.What is the divisibility rule for 171?

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2.How many numbers are there between 1 and 1000 that are divisible by 171?

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3.Is 513 divisible by 171?

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4.What if I get 0 after using the rule for 19?

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5.Does the divisibility rule of 171 apply to all integers?

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6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 171?

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7.What are some fun ways kids in United States can practice Divisibility Rule of 171 with numbers?

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8.What role do numbers and Divisibility Rule of 171 play in helping children in United States develop problem-solving skills?

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9.How can families in United States 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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About BrightChamps in United States

At BrightChamps, we believe numbers are more than symbols—they’re keys unlocking endless possibilities! Our goal is to help children across the United States build strong math skills, focusing today on the Divisibility Rule of 171 and especially on understanding the Divisibility Rule—delivered in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, keeping score during Little League games, or managing their allowance for the newest gadgets, knowing numbers boosts their confidence for real-life situations. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA learn in diverse ways, we customize our approach to match each learner’s style. From the lively streets of New York City to the sunny beaches of California, BrightChamps makes math relatable and exciting across America. Let’s make the Divisibility Rule an enjoyable part of every child’s math adventure!
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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.

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Fun Fact

: She loves to read number jokes and games.

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