Divisibility Rule of 11
2026-02-28 17:15 Diff
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Last updated on August 5, 2025

Divisibility rules are the guidelines to determine whether a number can be evenly divided by any specific number or not. In real life, we can use the divisibility rule used for mental math problems. This topic will cover the “Divisibility Rule of 11”.

What is the Divisibility Rule of 11?

The divisibility of 11 provides a simple way to check if any number is divisible by 11 without performing a long division method.


Step 1: Start from the leftmost digit and separate the digits based on even and odd position.


Step 2: Add the digits in even position and note the even sum.


Step 3: Add the digits in odd position and note the odd sum.


Step 4: Now, find the difference between Alternative sum (it is the sum of alternate digits). If the resulting difference is 0 or a multiple of 11, the number is divisible by 11.


Example: Let’s check whether the number 5863 is divisible by 11.


The digits in even positions are 8 and 3. The digits in odd positions are 5 and 6.


The sum of the digits in even positions is 8 + 3 = 11. The sum of the digits in odd positions is 5 + 6 = 11.


The difference between even sum and odd sum is 11 –  11 = 0. If the difference between even sum and odd sum of digits is 0 or multiples of 11 then the number is divisible by 11.
 

Tips and Tricks for Divisibility Rule of 11

Divisibility rules are quick tricks that make the division process easy for children. Let us see some tips and tricks for using divisibility rules of 11.

  • Know the Patterns

There are some numbers that follow a pattern with repeated digits. These will make it easy to check the divisibility rule.


Example: For example, numbers such as 121 or 1331 give us an alternating sum of 0, which makes children recognize that the number is divisible by 11 easily.

  • Working on Multiple Numbers

Practicing with multiple numbers will help children master the alternative sum approach. This will help children to identify which numbers are divisible by 11 in a short period.

  • Shortcuts with Multiples of 11

If children know that a number is already divisible by 11, then it is easy for them to know the multiples of that number are also divisible by 11.


Example: 77 is divisible by 11, the multiples of 77 such as 77, 154, 231,.., are also divisible by 11.
 

Common Mistakes and How to Avoid Them in Divisibility Rule of 11

Children might encounter some things while checking for divisibility of 11. Here are some mistakes that might be made by children.
 

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Problem 1

Check whether 121 is divisible by 11 or not.

Okay, lets begin

121 is divisible by 11.
 

Explanation

To check whether 121 is divisible by 11 or not, follow these steps.

  •  Add the digits in even positions: 2
  •  Add the digits in odd positions: 1+1
  • Find the difference: 2 – 2 = 0
  • The difference is 0 and if the result is 0 or multiple of 11 then the number is divisible by 11, hence the number 121 is divisible by 11.
     

Well explained 👍

Problem 2

A shop puts a sale on items whose price is divisible by 11. Is an item with a price $232 eligible for sale?

Okay, lets begin

No, an item with a price of $232 is not eligible for sale.

Explanation

To find out if the item is eligible for sale, we have to apply a divisibility of 11 on the number 232.

  • First, note the sum of digits in odd positions: 2 + 2 = 4
  • Add the digits in even positions: 3
  • Find the difference between even sum and odd sum = 4 – 3 = 1
  • Since 1 is not divisible by 11, the number 232 is not divisible by 11.
     

Well explained 👍

Problem 3

An employee needs to divide a 132-hour project into 11 equal shifts for a team. Find how many employees will be there in each team.

Okay, lets begin

There will be 12 employees in each team.

Explanation

To find out the number of employees per team, we have to check whether 132 is divisible by 11 or not.

  • Find out the sum of digits in odd positions: 2 + 1 = 3
  • Find the sum of digits in even positions: 3
  • Difference of sums = 3 – 3 = 0
  • The difference is 0 and if the result is 0 or multiple of 11 then the number is divisible by 11, hence 132 is divisible by 11 
  • The total employees per team = 132 / 11 = 12
     

Well explained 👍

FAQs on Divisibility Rule of 11

1.Is a number 123 divisible by 11?

 No, 123 is not divisible by 11 because the alternating sum of 123 is 4 – 2 = 2, which is not divisible by 11.
 

2.Mention some real-world applications of the divisibility rule of 11.

Some real-world applications of the divisibility rule of 11 are data analysis, inventory management, scheduling, and finance.
 

3. Is 10824 divisible by 11?

The alternating sum of 10824 (1+8+4) - 2 =13-2 = 11, which is divisible by 11. So, 10824 is also divisible by 11.
 

4. What if alternating sum is negative?

Even if the alternating sum is negative, it is valid. If the alternating sum of the number is divisible by 11 then the number is divisible by 11.
 

5.Is 132 divisible by both 2 and 11?

Yes, 132 is divisible by 2 because the one’s place digit is even, and it is divisible by 11 because the alternating sum is 3 – 3 = 0, which is divisible by 11.
 

Important Glossaries for Divisibility Rule of 11

  • Fractions: It is a part of the whole number, and it is always represented in the form of p/q where both p and q are integers and q ≠ 0. For example, ⅔ , ¾ 
  • Decimal: It is one of the types of numbers consisting of whole and fractional part separated by a decimal point. For example, 2.046 where 2 is the whole number and .046 is the fractional part.
  • Whole Numbers: The set of natural numbers, including zero, are called whole numbers. For example, 0, 1, 2, 3, … , are set of whole numbers.
  • Alternating Sum: The difference between the sum of digits in even place and the sum of digits in odd place of a number is called alternating sum. For example, alternating sum for 1334 is ((4–3) + (3–1)) = 3.
  • Multiple: Multiple is a result of multiplying a given number by an integer. For example, 21 is multiple because it is the result of 7  3.
     

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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.