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Last updated on May 26th, 2025

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Divisibility Rule of 11

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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”.

Divisibility Rule of 11 for UK Students
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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.
 

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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.
 

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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.
 

Mistake 1

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Leaving Some Digits in the Number While Calculating the Sums.
 

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Children might accidentally skip or miss some digits while calculating sum. For example, children might calculate the sum of, 2345 as 5 – 3 + 4 = 6(here 2 is missing ). But the correct sum is 5 – 3 + 4 – 2 = 4. Practicing with more numbers helps children not to make these mistakes.
 

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Divisibility Rule of 11 Examples

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Problem 1

Check whether 121 is divisible by 11 or not.

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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.
     

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Max, the Girl Character from BrightChamps

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?

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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.
     

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Max, the Girl Character from BrightChamps

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.

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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
     

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FAQs on Divisibility Rule of 11

1.Is a number 123 divisible by 11?

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

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3. Is 10824 divisible by 11?

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4. What if alternating sum is negative?

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5.Is 132 divisible by both 2 and 11?

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6.How can children in United Kingdom use numbers in everyday life to understand Divisibility Rule of 11?

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7.What are some fun ways kids in United Kingdom can practice Divisibility Rule of 11 with numbers?

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8.What role do numbers and Divisibility Rule of 11 play in helping children in United Kingdom develop problem-solving skills?

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9.How can families in United Kingdom create number-rich environments to improve Divisibility Rule of 11 skills?

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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.
     
Professor Greenline from BrightChamps

About BrightChamps in United Kingdom

At BrightChamps, we know numbers are more than just figures—they open doors to a world full of opportunities! Our mission is to assist children across the United Kingdom in mastering key math concepts, including today’s Divisibility Rule of 11, with a special emphasis on the Divisibility Rule—taught in a lively, enjoyable, and simple manner. Whether your child is measuring the speed of a roller coaster at Alton Towers, tracking scores at a local football match, or managing their pocket money for the latest gadgets, a solid grasp of numbers builds confidence for daily challenges. Our interactive lessons are designed to be both fun and accessible. Because children in the UK learn differently, we tailor our methods to suit every learner. From bustling London to Cornwall’s scenic coastlines, BrightChamps brings math to life, making it relevant and exciting across the UK. Let’s turn the Divisibility Rule into a fun part of every child’s math journey!
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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.

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Fun Fact

: She loves to read number jokes and games.

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