210 LearnersLast updated on May 26th, 2025
Divisibility Rule of 637
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 637.
What is the Divisibility Rule of 637?
The divisibility rule for 637 is a method by which we can find out if a number is divisible by 637 or not without using the division method. Check whether 1274 is divisible by 637 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2, here in 1274, 4 is the last digit. Multiply it by 2. 4 × 2 = 8
Step 2: Subtract the result from Step 1 from the remaining values without including the last digit. i.e., 127–8 = 119.
Step 3: As 119 is not a multiple of 637, the number is not divisible by 637. If the result from Step 2 were a multiple of 637, then the number would be divisible by 637.
Tips and Tricks for Divisibility Rule of 637
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 637.
Know the multiples of 637:
Memorize the multiples of 637 (637, 1274, 1911, 2548…etc.) to quickly check divisibility. If the result from the subtraction is a multiple of 637, then the number is divisible by 637.
Use the negative numbers:
If the result we get after the subtraction is negative, we will avoid the symbol and consider it as positive 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 637. For example: Check if 7648 is divisible by 637 using the divisibility test. Multiply the last digit by 2, i.e., 8 × 2 = 16.
Subtract the remaining digits excluding the last digit by 16, 764–16 = 748. Still, 748 is a large number, hence we will repeat the process again and multiply the last digit by 2, 8 × 2 = 16. Now subtracting 16 from the remaining numbers excluding the last digit, 74–16 = 58. As 58 is not a multiple of 637, 7648 is not divisible by 637.
Use the division method to verify:
Students can use the division method as a way to verify and crosscheck their results. This will help them to verify and also learn.
Common Mistakes and How to Avoid Them in Divisibility Rule of 637
The divisibility rule of 637 helps us quickly check if a given number is divisible by 637, but common mistakes like calculation errors can lead to incorrect conclusions. Here we will understand some common mistakes that will help you understand.
Mistake 1
Not following the correct steps.
Students should follow the correct steps: multiply the last digit by 2, then subtract the result from the remaining digits excluding the last digit, and check whether it is a multiple of 637.
Mistake 2
Including the last digit in subtraction.
Students should keep in mind that they should exclude the last digit while subtracting and include all the remaining digits.
Mistake 3
Not repeating the process when the result is large.
Students often stop the process after they have a large number after subtraction. The process should be repeated until we get the smallest number that is divisible by 637.
Mistake 4
Not considering the negative values.
Students consider the negative values, thinking divisibility rules don't apply to negative values. But the divisibility rule is applicable for negative values too. So students should consider the negative values as positive while checking for divisibility.
Mistake 5
Confusing the steps.
Students often confuse the steps or forget them. To avoid this error, students should practice regularly.
Divisibility Rule of 637 Examples
Problem 1
Is 3812 divisible by 637?
Yes, 3812 is divisible by 637.
Explanation
To check if 3812 is divisible by 637, let's use this unique divisibility rule:
1) Consider the last three digits, which form the number 812.
2) Subtract twice the number formed by the remaining digits (3) from 812.
3) 812 - 2 × 3 = 812 - 6 = 806.
4) Check if 806 is a multiple of 637. Yes, 806 ÷ 637 = 1.264, so 3812 is divisible by 637.
Problem 2
Check the divisibility rule of 637 for 1274.
No, 1274 is not divisible by 637.
Explanation
To verify if 1274 is divisible by 637, follow these steps:
1) Consider the last three digits, which form the number 274.
2) Subtract twice the number formed by the remaining digits (1) from 274.
3) 274 - 2 × 1 = 274 - 2 = 272.
4) Check if 272 is a multiple of 637. No, 272 ÷ 637 = 0.426, so 1274 is not divisible by 637.
Problem 3
Is -2548 divisible by 637?
No, -2548 is not divisible by 637.
Explanation
To determine if -2548 is divisible by 637, we ignore the negative sign for the test.
1) Consider the last three digits, which form the number 548.
2) Subtract twice the number formed by the remaining digits (2) from 548.
3) 548 - 2 × 2 = 548 - 4 = 544.
4) Check if 544 is a multiple of 637. No, 544 ÷ 637 = 0.854, so -2548 is not divisible by 637.
Problem 4
Can 7642 be divisible by 637 following the divisibility rule?
Yes, 7642 is divisible by 637.
Explanation
To check if 7642 is divisible by 637, follow these steps:
1) Consider the last three digits, which form the number 642.
2) Subtract twice the number formed by the remaining digits (7) from 642.
3) 642 - 2 × 7 = 642 - 14 = 628.
4) Check if 628 is a multiple of 637. Yes, 628 ÷ 637 = 0.985, so 7642 is divisible by 637.
Problem 5
Check the divisibility rule of 637 for 3185.
No, 3185 is not divisible by 637.
Explanation
To check the divisibility of 3185 by 637, proceed with the following steps:
1) Consider the last three digits, which form the number 185.
2) Subtract twice the number formed by the remaining digits (3) from 185.
3) 185 - 2 × 3 = 185 - 6 = 179.
4) Check if 179 is a multiple of 637. No, 179 ÷ 637 = 0.281, so 3185 is not divisible by 637
FAQs on Divisibility Rule of 637
1.What is the divisibility rule for 637?
2.How many numbers are there between 1 and 5000 that are divisible by 637?
3. Is 1911 divisible by 637?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 637 apply to all integers?
6.How can children in Australia use numbers in everyday life to understand Divisibility Rule of 637?
7.What are some fun ways kids in Australia can practice Divisibility Rule of 637 with numbers?
8.What role do numbers and Divisibility Rule of 637 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Divisibility Rule of 637 skills?
Important Glossaries for Divisibility Rule of 637:
- Divisibility rule: The set of rules used to find out whether a number is divisible by another number or not.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 637 are 637, 1274, 1911, 2548, etc.
- Integers: Integers are the numbers that include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is a process of finding the difference between two numbers by reducing one number from another.
- Verification: The process of confirming the correctness of a result, often by checking with an alternative method, such as using division to verify divisibility.
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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.
