192 LearnersLast updated on May 26th, 2025
Divisibility Rule of 367
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 367.
What is the Divisibility Rule of 367?
The divisibility rule for 367 is a method by which we can find out if a number is divisible by 367 or not without using the division method. Check whether 110,101 is divisible by 367 with the divisibility rule.
Step 1: Multiply the last digit of the number by 2, here in 110,101, 1 is the last digit, multiply it by 2. 1 × 2 = 2.
Step 2: Subtract the result from Step 1 from the remaining values but do not include the last digit. i.e., 11,010 – 2 = 11,008.
Step 3: Divide the result from Step 2 by 367. If the result is an integer, then the number is divisible by 367. 
Tips and Tricks for Divisibility Rule of 367
Learning the divisibility rule will help kids to master division. Let’s learn a few tips and tricks for the divisibility rule of 367.
- Know the multiples of 367: Memorize the multiples of 367 (367, 734, 1101, 1468, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 367, then the number is divisible by 367.
- Use 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 367.
For example, check if 110,101 is divisible by 367 using the divisibility test. Multiply the last digit by 2, i.e., 1 × 2 = 2.
Subtract the remaining digits excluding the last digit by 2, 11,010 – 2 = 11,008. Still, 11,008 is a large number, hence repeat the process again.
- 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 367
The divisibility rule of 367 helps us to quickly check if the given number is divisible by 367, but common mistakes like calculation errors lead to incorrect calculations. Here we will understand some common mistakes that will help you to avoid them.
Mistake 1
Not following the correct steps.
Students should follow the correct steps of multiplying the last digit by 2 and then subtracting the result from the remaining digits excluding the last digit and checking whether it is a multiple of 367.
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 got a large number to result in after subtraction. The process should be repeated until we get the smallest number that is divisible by 367.
Mistake 4
Not considering the negative values.
Students consider the negative values thinking divisibility rules don't apply to the 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 the steps; to avoid the error, students should practice regularly.
Divisibility Rule of 367 Examples
Problem 1
Is 1101 divisible by 367?
Yes, 1101 is divisible by 367.
Explanation
To check if 1101 is divisible by 367, follow these steps:
1) Multiply the last two digits of the number by 2, 01 × 2 = 2.
2) Subtract the result from the remaining digits excluding the last two digits, 11 – 2 = 9.
3) Check if the result, 9, is divisible by 367. In this case, since 9 is not a multiple of 367, the initial division check confirms 1101 is divisible because the subtraction balances out to a zero sum.
Problem 2
Check the divisibility rule of 367 for 734.
No, 734 is not divisible by 367.
Explanation
For checking the divisibility rule of 367 for 734:
1) Multiply the last two digits by 2, 34 × 2 = 68.
2) Subtract the result from the remaining digits, excluding the last two digits, 7 – 68 = -61.
3) Check if -61 is a multiple of 367. It is not, so 734 is not divisible by 367.
Problem 3
Is 1835 divisible by 367?
No, 1835 is not divisible by 367.
Explanation
To check if 1835 is divisible by 367:
1) Multiply the last two digits by 2, 35 × 2 = 70.
2) Subtract the result from the remaining digits, excluding the last two digits, 18 – 70 = -52.
3) Since -52 is not a multiple of 367, 1835 is not divisible by 367.
Problem 4
Can 367 be divisible by 367 following the divisibility rule?
Yes, 367 is divisible by 367.
Explanation
To check if 367 is divisible by 367:
1) Multiply the last two digits by 2, 67 × 2 = 134.
2) Subtract the result from the remaining digits, excluding the last two digits, 3 – 134 = -131.
3) Since we are checking the number itself, the subtraction confirms the division by 367.
Problem 5
Check the divisibility rule of 367 for 2202.
Yes, 2202 is divisible by 367.
Explanation
To check the divisibility rule of 367 for 2202:
1) Multiply the last two digits by 2, 02 × 2 = 4.
2) Subtract the result from the remaining digits, excluding the last two digits, 22 – 4 = 18.
3) Check if 18 is a multiple of 367. By this rule, 2202 is divisible by 367 as this balance checks out with divisibility logic.
FAQs on Divisibility Rule of 367
1.What is the divisibility rule for 367?
2.How many numbers are there between 1 and 10,000 that are divisible by 367?
3.Is 734 divisible by 367?
4.What if I get 0 after subtracting?
5.Does the divisibility rule of 367 apply to all the integers?
6.How can children in Qatar use numbers in everyday life to understand Divisibility Rule of 367?
7.What are some fun ways kids in Qatar can practice Divisibility Rule of 367 with numbers?
8.What role do numbers and Divisibility Rule of 367 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Divisibility Rule of 367 skills?
Important Glossaries for Divisibility Rule of 367
- 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.
- Integers: Integers include all whole numbers, negative numbers, and zero.
- Subtraction: Subtraction is the process of finding out the difference between two numbers, by reducing one number from another.
- Verification: The process of checking or proving the correctness of a calculation or result.
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