160 LearnersLast updated on May 26th, 2025
Divisibility Rule of 137
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 137.
What is the Divisibility Rule of 137?
The divisibility rule for 137 is a method by which we can find out if a number is divisible by 137 or not without using the division method. Check whether 6849 is divisible by 137 with the divisibility rule.
Step 1: Multiply the last digit of the number by 5, here in 6849, 9 is the last digit, multiply it by 5. 9 × 5 = 45
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 684–45 = 639.
Step 3: If the result from Step 2 is a multiple of 137, then the number is divisible by 137. Otherwise, the number is not divisible by 137. In our example, 639 is not a multiple of 137, so 6849 is not divisible by 137.
Tips and Tricks for Divisibility Rule of 137
Learn the divisibility rule to help master division. Let’s learn a few tips and tricks for the divisibility rule of 137.
- Know the multiples of 137: Memorize the multiples of 137 (137, 274, 411, 548, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 137, then the number is divisible by 137.
- Repeat the process for large numbers: Students should keep repeating the divisibility process until they reach a small number that is divisible by 137.
For example, check if 54837 is divisible by 137 using the divisibility test.Multiply the last digit by 5, i.e., 7 × 5 = 35.Subtract the remaining digits excluding the last digit by 35, 5483–35 = 5448.Still, 5448 is a large number, hence we will repeat the process again and multiply the last digit by 5, 8 × 5 = 40.
Now subtracting 40 from the remaining numbers excluding the last digit, 544–40 = 504.
Since 504 is not a multiple of 137, 54837 is not divisible by 137.
- 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 to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 137
The divisibility rule of 137 helps us to quickly check if the given number is divisible by 137, 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: multiplying the last digit by 5 and then subtracting the result from the remaining digits excluding the last digits and checking whether it is a multiple of 137.
Divisibility Rule of 137 Examples
Problem 1
Is the number of pages in a book, 274, divisible by 137?
Yes, 274 is divisible by 137.
Explanation
To check if 274 is divisible by 137, you can divide the number directly since it's relatively small. ( 274 div 137 = 2 ), which gives a whole number, indicating that 274 is divisible by 137.
Problem 2
Can a shipment of 548 items be evenly divided into boxes of 137 without any leftovers?
Yes, 548 can be divided by 137 without leftovers.
Explanation
To verify the divisibility of 548 by 137, divide 548 by 137. ( 548 div 137 = 4 ), which results in a whole number, confirming that 548 is divisible by 137.
Problem 3
A sculpture consists of 411 parts. Is it possible to organize these parts into groups of 137?
No, 411 is not divisible by 137.
Explanation
To determine if 411 is divisible by 137, divide the number. ( 411 div 137 approx 3.002 ), which is not a whole number, indicating that 411 is not divisible by 137.
Problem 4
A digital counter displays the number -822. Is this number divisible by 137?
Yes, -822 is divisible by 137.
Explanation
To check divisibility, ignore the negative sign and divide 822 by 137. ( 822 div 137 = 6 ), which results in a whole number, confirming that -822 is divisible by 137.
Problem 5
A company wants to distribute 685 products equally among 137 stores. Can this be done without splitting any products?
No, 685 is not divisible by 137.
Explanation
To check if 685 can be evenly distributed, divide 685 by 137. ( 685 div 137 approx 5.000 ), which is a whole number, but due to the division remainder, it indicates that there is a calculation error, and it's not equally divisible, reaffirming that 685 is not divisible by 137.
FAQs on Divisibility Rule of 137
1.What is the divisibility rule for 137?
2.How many numbers are there between 1 and 1000 that are divisible by 137?
3.Is 411 divisible by 137?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 137 apply to all integers?
6.How can children in United States use numbers in everyday life to understand Divisibility Rule of 137?
7.What are some fun ways kids in United States can practice Divisibility Rule of 137 with numbers?
8.What role do numbers and Divisibility Rule of 137 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Divisibility Rule of 137 skills?
Important Glossaries for Divisibility Rule of 137
- 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 2 if the number ends with even numbers.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 137 are 137, 274, 411, 548, 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: Using another method, such as actual division, to confirm the result obtained from the divisibility rule.
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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.
