Shortcut for Divisibility by 11

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Shortcut for Divisibility by 11DIVIBILITY RULE OF 11 Alternating sum of digits is divisible by 11 (or 0). EXAMPLE: 12353 Odd (1st): Even (2nd): Odd (3rd): Even (4th): Odd (5th): Sum of odd digits: Sum of even digits: Sum of odd - Sum of even: 7-7 = (V) 0 is divisible by 11 So, 12353 is divisible by 11. So, we can write it as If So, if the difference is 0, 11, 22, 33, …. Then, Number is divisible by 11 Note: We start counting from the right as it makes it easier Is 308 divisible by 11? 308 Sum of digits at Odd places Sum of digits at Even places Difference = 11 − 0 = 11 Since 11 is divisible by 11 ∴ 308 is divisible by 11 Is 1331 divisible by 11? 1 3 3 1 Sum of digits at Odd places Sum of digits at Even places Difference = 4 − 4 = 0 Since difference is 0 ∴ 1331 is divisible by 11 Is 61809 divisible by 11? 6 1 8 0 9 Sum of digits at Odd places Sum of digits at Even places Difference = 23 − 1 = 22 Since 22 is divisible by 11 ∴ 61809 is divisible by 11 Is 5081 divisible by 11? 5 0 8 1 Sum of digits at Odd places Sum of digits at Even places Difference = 13 − 1 = 12 Since 12 is not divisible by 11 ∴ 5081 is not divisible by 11