Which Number is Divisible by 11?

Many numbers are divisible by 11! To determine if a specific number is divisible by 11, we can use several methods.

Understanding Divisibility by 11

A number is divisible by 11 if it meets certain criteria. Here are two common methods:

Method 1: Alternating Sum of Digits

• This method involves calculating the alternating sum of the digits. Starting from the rightmost digit, alternately add and subtract digits. If the result is divisible by 11 (including 0), the original number is also divisible by 11.

  • Example: Let's consider the number 2728.
    1. 8 - 2 + 7 - 2 = 11
    2. Since 11 is divisible by 11, 2728 is divisible by 11.

Method 2: Difference of Digit Sums (Odd vs. Even Places)

• Alternatively, find the sum of digits in odd places and the sum of digits in even places. Subtract the smaller sum from the larger sum. If the result is 0 or a multiple of 11, the number is divisible by 11.

  • Example: For the number 91827,
    1. Sum of digits in odd places (from right to left): 7 + 8 + 9 = 24
    2. Sum of digits in even places: 2 + 1 = 3
    3. Difference: 24 - 3 = 21. 21 is not divisible by 11, so 91827 is not divisible by 11.

Examples of Numbers Divisible by 11

• Small numbers: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132... (as stated in the provided text). These are all multiples of 11.
• Larger numbers: Many larger numbers are also divisible by 11. Using the methods above, you can easily determine if any number is divisible by 11.

To reiterate from the provided resources: The divisibility rule for 11 states that a number is divisible by 11 if the alternating sum of its digits is divisible by 11 or if the difference between the sum of digits in odd places and the sum of digits in even places is 0 or a multiple of 11.