214 LearnersLast updated on May 26th, 2025
Divisibility Rule of 311
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 311.
What is the Divisibility Rule of 311?
The divisibility rule for 311 is a method by which we can find out if a number is divisible by 311 or not without using the division method. Check whether 4665 is divisible by 311 with the divisibility rule.
Step 1: Multiply the last digit of the number by 3, here in 4665, 5 is the last digit, multiply it by 3. 5 × 3 = 15.
Step 2: Subtract the result from Step 1 from the remaining values, but do not include the last digit. i.e., 466–15 = 451.
Step 3: As it is shown that 451 is not a multiple of 311, the number is not divisible by 311. If the result from step 2 is a multiple of 311, then the number is divisible by 311.
Tips and Tricks for Divisibility Rule of 311
Learning the divisibility rule will help kids master division. Let’s learn a few tips and tricks for the divisibility rule of 311.
Know the multiples of 311:
Memorize the multiples of 311 (311, 622, 933, 1244, etc.) to quickly check the divisibility. If the result from the subtraction is a multiple of 311, then the number is divisible by 311.
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 easily checked for divisibility by 311.
For example: Check if 9328 is divisible by 311 using the divisibility test.
Multiply the last digit by 3, i.e., 8 × 3 = 24.
Subtract the remaining digits excluding the last digit by 24, 932–24 = 908.
Still, 908 is a large number, hence we will repeat the process again and multiply the last digit by 3, 8 × 3 = 24.
Now subtracting 24 from the remaining numbers excluding the last digit, 90–24 = 66.
As 66 is not a multiple of 311, 9328 is not divisible by 311.
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 311
The divisibility rule of 311 helps us to quickly check if the given number is divisible by 311, but common mistakes like calculation errors lead to incorrect answers. 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 that are multiplying the last digit by 3 and then subtracting the result from the remaining digits excluding the last digit, and checking whether it is a multiple of 311.
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 after subtraction. The process should be repeated until we get the smallest number that is easily checked for divisibility by 311.
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 the steps. To avoid this error, students should practice regularly.
Divisibility Rule of 311 Examples
Problem 1
Can 9331 be divisible by 311?
Yes, 9331 is divisible by 311
Explanation
To determine if 9331 is divisible by 311:
1) Rearrange the digits to form a new number: 139.
2) Check if this new number is divisible by 311. Since 139 is not divisible by 311, we need further checks.
3) Multiply 139 by 311: 139 × 311 = 43269.
4) The original number 9331 is part of this multiplication process and aligns with 311’s divisibility since 139 is an integral part of its calculation.
Problem 2
Is 622 divisible by 311?
Yes, 622 is divisible by 311.
Explanation
To check divisibility:
1) Rearrange the digits of 622 to form 226.
2) Multiply this number by 311: 226 × 311 = 70386.
3) Since 70386 is a valid multiple of 311 and 226 was used in this calculation, it shows 622 is divisible by 311.
Problem 3
Determine if -1555 is divisible by 311.
No, -1555 is not divisible by 311.
Explanation
For checking a negative number like -1555:
1) Remove the negative sign and rearrange digits to form 515.
2) Check if 515 is divisible by 311. Since 515 divided by 311 does not yield an integer, -1555 is not divisible by 311
Problem 4
Evaluate the divisibility of 4442 by 311.
No, 4442 is not divisible by 311
Explanation
To assess the divisibility:
1) Rearrange the digits to form 424.
2) Multiply this number by 311: 424 × 311 = 131864.
3) Since 131864 is not related to the original number 4442, 4442 is not divisible by 311.
Problem 5
Is 1555 divisible by 311?
Yes, 1555 is divisible by 311.
Explanation
For checking:
1) Rearrange the digits to form 551.
2) Multiply 551 by 311: 551 × 311 = 171311.
3) Since 171311 aligns with the original number 1555 by the multiplication process, it confirms divisibility by 311.
FAQs on Divisibility Rule of 311
1. What is the divisibility rule for 311?
2. How many numbers are there between 1 and 1000 that are divisible by 311?
3. Is 622 divisible by 311?
4. What if I get 0 after subtracting?
5. Does the divisibility rule of 311 apply to all integers?
6.How can children in Vietnam use numbers in everyday life to understand Divisibility Rule of 311?
7.What are some fun ways kids in Vietnam can practice Divisibility Rule of 311 with numbers?
8.What role do numbers and Divisibility Rule of 311 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Divisibility Rule of 311 skills?
Important Glossaries for Divisibility Rule of 311
- 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 311 if it follows the specific procedure outlined.
- Multiples: Multiples are the results we get after multiplying a number by an integer. For example, multiples of 311 are 311, 622, 933, 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: The process of confirming the correctness of a result through an independent method, such as direct division.
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About BrightChamps in Vietnam
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.
