Study Guides/Maths/Divisibility Rule of 11
Study Guide · Maths

What is the Divisibility Rule of 11?

When working with massive numbers in math exams, doing a full long division to check if a number is divisible by 11 takes too much time. Luckily, there is a brilliant mathematical shortcut.

The Divisibility Rule of 11 states: If the absolute difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11 (like 11, 22, 33), then the entire massive number is perfectly divisible by 11.

Question (Click to Flip)

What is the divisibility rule of 11?

Answer

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is 0 or a multiple of 11.

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Key Facts

Rule: Difference between (Sum of odd places) and (Sum of even places).

Success Condition: The difference must equal 0, 11, 22, 33, etc.

Failure Condition: If the difference is any other number, it is not divisible.

Speed: This mental math trick is 10x faster than doing long division on paper.

Step-by-Step Method

Follow these 4 simple steps:

  1. Write down the large number.
  2. Add together every alternate digit starting from the first digit (Sum of Odd positions).
  3. Add together the remaining alternate digits (Sum of Even positions).
  4. Subtract the smaller sum from the larger sum to find the difference. If the answer is 0 or 11 (or 22, 33), the number is divisible by 11. If you get any other number (like 3 or 7), it is not.

Solved Example 1: Is 1364 divisible by 11?

  • Step 1: The number is 1 3 6 4.
  • Step 2: Add digits in odd positions (1st and 3rd digits): 1 + 6 = 7.
  • Step 3: Add digits in even positions (2nd and 4th digits): 3 + 4 = 7.
  • Step 4: Find the difference: 7 - 7 = 0. Since the difference is 0, the number 1364 IS divisible by 11.

Solved Example 2: Is 2728 divisible by 11?

  • Step 1: The number is 2 7 2 8.
  • Step 2: Sum of odd positions: 2 + 2 = 4.
  • Step 3: Sum of even positions: 7 + 8 = 15.
  • Step 4: Find the difference: 15 - 4 = 11. Since the difference is exactly 11, the number 2728 IS divisible by 11.

Questions and Answers

What is the divisibility rule of 11?+

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is 0 or a multiple of 11.

Is 121 divisible by 11?+

Yes. Odd positions (1+1=2). Even position (2). Difference is 2-2=0. Therefore, it is divisible by 11.

Does this rule work for any size number?+

Yes, this rule works flawlessly whether the number is 3 digits long or 30 digits long.

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