What are all the 5-digit multiples of 11?

Answer 1

-6

Answer 2

10000 ÷ 11 = 909 r 1 → first 5-digit multiple of 11 is 11 × 910 = 10010

99999 ÷ 11 = 9090 r 9 → last 5-digit multiple of 11 is 11 × 9090 = 99990

→ there are 9090 - 910 + 1 = 8181 5-digit multiples of 11.

The first 100 are:

10010, 10021, 10032, 10043, 10054, 10065, 10076, 10087, 10098, 10109, 10120, 10131, 10142, 10153, 10164, 10175, 10186, 10197, 10208, 10219, 10230, 10241, 10252, 10263, 10274, 10285, 10296, 10307, 10318, 10329, 10340, 10351, 10362, 10373, 10384, 10395, 10406, 10417, 10428, 10439, 10450, 10461, 10472, 10483, 10494, 10505, 10516, 10527, 10538, 10549, 10560, 10571, 10582, 10593, 10604, 10615, 10626, 10637, 10648, 10659, 10670, 10681, 10692, 10703, 10714, 10725, 10736, 10747, 10758, 10769, 10780, 10791, 10802, 10813, 10824, 10835, 10846, 10857, 10868, 10879, 10890, 10901, 10912, 10923, 10934, 10945, 10956, 10967, 10978, 10989, 11000, 11011, 11022, 11033, 11044, 11055, 11066, 11077, 11088, 11099, ...

The last 100 are:

..., 98901, 98912, 98923, 98934, 98945, 98956, 98967, 98978, 98989, 99000, 99011, 99022, 99033, 99044, 99055, 99066, 99077, 99088, 99099, 99110, 99121, 99132, 99143, 99154, 99165, 99176, 99187, 99198, 99209, 99220, 99231, 99242, 99253, 99264, 99275, 99286, 99297, 99308, 99319, 99330, 99341, 99352, 99363, 99374, 99385, 99396, 99407, 99418, 99429, 99440, 99451, 99462, 99473, 99484, 99495, 99506, 99517, 99528, 99539, 99550, 99561, 99572, 99583, 99594, 99605, 99616, 99627, 99638, 99649, 99660, 99671, 99682, 99693, 99704, 99715, 99726, 99737, 99748, 99759, 99770, 99781, 99792, 99803, 99814, 99825, 99836, 99847, 99858, 99869, 99880, 99891, 99902, 99913, 99924, 99935, 99946, 99957, 99968, 99979, 99990.

The other 7981 in between are left as an exercise for the reader.