184 LearnersLast updated on May 26th, 2025
Divisibility Rule of 172
The divisibility rule is a way to determine 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 172.
What is the Divisibility Rule of 172?
The divisibility rule for 172 is a method by which we can find out if a number is divisible by 172 without using the division method. Check whether 51616 is divisible by 172 with the divisibility rule.
Step 1: Break the number into groups of three digits starting from the right. Here, 51616 becomes two groups: 016 and 51.
Step 2: Calculate each group's remainder when divided by 172. For instance, 016 divided by 172 has a remainder of 16, and 51 divided by 172 has a remainder of 51.
Step 3: Multiply the remainder of the left group (51 in this example) by 1000 (since it's the next power of 10) and add the remainder of the right group. This gives us 51000 + 16 = 51016.
Step 4: Check if the result is divisible by 172. Here, 51016 is not divisible by 172.
If the result from step 3 is divisible by 172, then the entire number is divisible by 172. If not, then the number isn't divisible by 172.
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Tips and Tricks for Divisibility Rule of 172
Learning the divisibility rule helps in mastering division. Let’s explore a few tips and tricks for the divisibility rule of 172.
- Know the multiples of 172: Memorize the multiples of 172 (172, 344, 516, 688, etc.) to quickly check divisibility. If the result from the calculation is a multiple of 172, then the number is divisible by 172.
- Use negative numbers: If the result we get is negative, consider it as positive for checking divisibility.
- Repeat the process for large numbers: Continue the divisibility process until you reach a small number that is divisible by 172.
- Use the division method to verify: Cross-check results using the division method to verify and learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 172
The divisibility rule of 172 helps us check if a number is divisible by 172, but common mistakes like calculation errors can lead to incorrect results. Here, we will understand some common mistakes and how to avoid them.
Mistake 1
Not following the correct steps.
Ensure that you break the number into groups, find remainders, and perform the calculations correctly.
Mistake 2
Forgetting to multiply the remainder by 1000.
Remember to multiply the left group's remainder by 1000 before adding the remainders.
Mistake 3
Not repeating the process for large results.
Repeat the process until you obtain a small number that can easily be checked for divisibility by 172.
Mistake 4
Ignoring negative results.
Treat negative results as positive when checking for divisibility.
Mistake 5
Confusing the steps.
Regular practice helps in remembering and applying the steps correctly.
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Divisibility Rule of 172 Examples
Problem 1
A train consists of 172 carriages. Is the total number of carriages divisible by 172?
Yes, 172 is divisible by 172.
Explanation
To check divisibility by 172, if the number itself is 172, it obviously divides evenly into itself with no remainder. Therefore, the total number of carriages is divisible by 172.
Problem 2
A factory produces 344 units of a product every day. Can these units be perfectly packed into boxes containing 172 units each?
Yes, 344 is divisible by 172.
Explanation
For checking divisibility by 172, divide 344 by 172. The result is exactly 2, indicating that 344 can be divided into two equal parts of 172 with no remainder.
Problem 3
A sports club has 516 members. Can these members be divided into equal groups of 172?
No, 516 is not divisible by 172.
Explanation
To determine if 516 can be divided into equal groups of 172, divide 516 by 172. The result is approximately 3.001, indicating there is a remainder, hence 516 is not divisible by 172.
Problem 4
A library has 688 books. Can these books be arranged evenly in shelves of 172 books each?
Yes, 688 is divisible by 172.
Explanation
To check the divisibility of 688 by 172, divide 688 by 172. The result is exactly 4, meaning the books can be perfectly arranged in shelves with no books left over.
Problem 5
A concert hall has 860 seats and wants to group them into sections of 172 seats. Is this possible?
No, 860 is not divisible by 172.
Explanation
To determine if 860 can be divided into sections of 172, divide 860 by 172. The result is approximately 5.0, indicating a remainder, hence 860 is not divisible by 172.
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FAQs on Divisibility Rule of 172
1.What is the divisibility rule for 172?
2.How many numbers are there between 1 and 1000 that are divisible by 172?
3.Is 344 divisible by 172?
4.What if I get 0 after the calculation?
5.Does the divisibility rule of 172 apply to all integers?
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Important Glossaries for Divisibility Rule of 172
- Divisibility rule: A set of rules used to find out whether a number is divisible by another without direct division.
- Multiples: Numbers obtained by multiplying a given number by integers. For example, multiples of 172 are 172, 344, 516, etc.
- Remainder: The amount left after division.
- Integers: Whole numbers, including positive, negative numbers, and zero.
- Calculation: A mathematical determination of size or number.
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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.
