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.
 

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.
 

• 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.