11divisibility

The divisibility rule for 11 provides a quick method to determine if an integer is divisible by 11. To apply this rule, one calculates the alternating sum of the digits of the number. Starting with the rightmost digit, add the first digit, subtract the second digit, add the third digit, and so on, moving from right to left. If the resulting sum is divisible by 11 (which includes 0, 11, -11, 22, -22, etc.), then the original number is also divisible by 11.

For example, consider the number 1353. The alternating sum of its digits is 3 - 5 + 3 - 1 = 0. Since 0 is divisible by 11, the number 1353 is divisible by 11. Another example is 2728. The alternating sum is 8 - 2 + 7 - 2 = 11. As 11 is divisible by 11, 2728 is also divisible by 11. If the alternating sum is not divisible by 11, the original number is not divisible by 11. For instance, in the number 1234, the alternating sum is 4 - 3 + 2 - 1 = 2. Since 2 is not divisible by 11, neither is 1234. This rule works for any integer, regardless of its size.