How do you know if a number is divisible by 11?

To determine if a number is divisible by 11, you can follow this simple rule:

• Alternating Sum: Calculate the alternating sum of the digits in the number, starting from the rightmost digit. This means you add the first digit, subtract the second digit, add the third, subtract the fourth, and so on.
• Divisible by 11: If the result of this alternating sum is divisible by 11, then the original number is also divisible by 11.

Example:

Let's consider the number 12321.

1. Alternating Sum: 1 - 2 + 3 - 2 + 1 = 1
2. Divisible by 11: Since 1 is not divisible by 11, the original number 12321 is also not divisible by 11.

Practical Insights:

• This rule applies to both positive and negative numbers.
• If the alternating sum is zero, the original number is divisible by 11.
• You can apply this rule repeatedly to large numbers by focusing on a smaller portion of the digits.

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