266 LearnersLast updated on May 26th, 2025
Divisibility Rule of 37
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 divisibility rules for quick math, dividing things evenly, and sorting things. In this topic, we will learn about the divisibility rule of 37.
What is the Divisibility Rule of 37?
The divisibility rule for 37 is a method by which we can find out if a number is divisible by 37 or not without using the division method. Check whether 111 is divisible by 37 with the divisibility rule.
Step 1: Multiply the last digit of the number by 3, here in 111, 1 is the last digit; multiply it by 3. 1 × 3 = 3
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 11 - 3 = 8.
Step 3: As 8 is not a multiple of 37, 111 is not divisible by 37. If the result from step 2 is a multiple of 37, then the number is divisible by 37.
Tips and Tricks for Divisibility Rule of 37
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 37.
- Know the multiples of 37: Memorize the multiples of 37 (37, 74, 111, 148, etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 37, then the number is divisible by 37.
- Use negative numbers: If the result after subtraction is negative, consider its absolute value 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 37.
For example: Check if 1480 is divisible by 37 using the divisibility test.
Multiply the last digit by 3, i.e., 0 × 3 = 0.
Subtract the result from the remaining digits excluding the last digit, 148 - 0 = 148.
Still, 148 is a large number, so we will repeat the process. Multiply the last digit by 3, 8 × 3 = 24.
Now subtract 24 from the remaining numbers excluding the last digit, 14 - 24 = -10.
The absolute value of -10 is not a multiple of 37, so 1480 is not divisible by 37.
- 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 37
The divisibility rule of 37 helps us quickly check if a given number is divisible by 37, 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.
Students should follow the correct steps: multiply the last digit by 3, subtract the result from the remaining digits excluding the last digit, and check whether it is a multiple of 37.
Divisibility Rule of 37 Examples
Problem 1
Is 148 divisible by 37?
No, 148 is not divisible by 37.
Explanation
To check if 148 is divisible by 37, we use a test:
1) Double the last digit of the number, 8 × 2 = 16.
2) Subtract this from the remaining digits, 14 - 16 = -2.
3) Since -2 is not a multiple of 37, 148 is not divisible by 37.
Problem 2
Check the divisibility rule of 37 for 481.
Yes, 481 is divisible by 37.
Explanation
To determine if 481 is divisible by 37:
1) Double the last digit, 1 × 2 = 2.
2) Subtract from the remaining digits, 48 - 2 = 46.
3) Since 46 is a multiple of 37 (37 × 1 + 9 = 46), 481 is divisible by 37.
Problem 3
Is -555 divisible by 37?
No, -555 is not divisible by 37.
Explanation
To check if -555 is divisible by 37, we consider the positive value 555:
1) Double the last digit, 5 × 2 = 10.
2) Subtract from the remaining digits, 55 - 10 = 45.
3) Since 45 is not a multiple of 37, -555 is not divisible by 37.
Problem 4
Can 1111 be divisible by 37?
No, 1111 is not divisible by 37.
Explanation
To verify if 1111 is divisible by 37:
1) Double the last digit, 1 × 2 = 2.
2) Subtract from the remaining digits, 111 - 2 = 109.
3) Since 109 is not a multiple of 37, 1111 is not divisible by 37.
Problem 5
Check the divisibility rule of 37 for 5929.
Yes, 5929 is divisible by 37.
Explanation
To check divisibility for 5929:
1) Double the last digit, 9 × 2 = 18.
2) Subtract from the remaining digits, 592 - 18 = 574.
3) Since 574 is a multiple of 37 (37 × 15 + 19 = 574), 5929 is divisible by 37.
FAQs on Divisibility Rule of 37
1.What is the divisibility rule for 37?
2.How many numbers are there between 1 and 200 that are divisible by 37?
3.Is 111 divisible by 37?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 37 apply to all integers?
6.How can children in India use numbers in everyday life to understand Divisibility Rule of 37?
7.What are some fun ways kids in India can practice Divisibility Rule of 37 with numbers?
8.What role do numbers and Divisibility Rule of 37 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 37 skills?
Important Glossaries for Divisibility Rule of 37
- 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 it ends with an even digit.
- Multiples: Multiples are the results obtained after multiplying a number by an integer. For example, multiples of 37 are 37, 74, 111, 148, and so on.
- Integers: Integers are numbers that include all the whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding the difference between two numbers by reducing one number from another.
- Absolute value: The absolute value of a number is its non-negative value without regard to its sign.
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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.
