Using this shortcut, find out whether the following numbers are divisible by 11. Further, find the remainder if the number is not divisible by 11.
158
841
481
Not divisible by 11. Alternating sum: 1 - 8 + 4 = -3. Remainder is 8 (or 3 less than a multiple of 11).
5529
90904
857076
Explanation
(i) For 158: Alternating sum = 8 - 5 + 1 = 4. Since 4 is not divisible by 11, 158 is not divisible by 11. The remainder when 158 is divided by 11 is 4. (ii) For 841: Alternating sum = 1 - 4 + 8 = 5. Since 5 is not divisible by 11, 841 is not divisible by 11. The remainder is 5. (iii) For 481: Alternating sum = 1 - 8 + 4 = -3. Since -3 is not divisible by 11, 481 is not divisible by 11. The remainder is 8 (or equivalently, 481 is 8 more than a multiple of 11). (iv) For 5529: Alternating sum = 9 - 2 + 5 - 5 = 7. Since 7 is not divisible by 11, 5529 is not divisible by 11. The remainder is 7. (v) For 90904: Alternating sum = 4 - 0 + 9 - 0 + 9 = 22. Since 22 is divisible by 11, 90904 is divisible by 11. 90904 ÷ 11 = 8264. (vi) For 857076: Alternating sum = 6 - 7 + 0 - 7 + 5 - 8 = -11. Since -11 is divisible by 11, 857076 is divisible by 11. 857076 ÷ 11 = 77916.