I did this problem in two steps. First I generated a list of all the palendromes that could work for this problem. I made sure it was in descending order so I could go through them more quickly. I then made a list, again in descending order, of all the 3 digit numbers that could be divisors.
Second, I divided each of the palendromes by each of the possible divisors. I had the program only show me those answers that resulted in integers.
set pal_set to {997799, 996699, 995599, 994499, 993399, 992299, 991199, 990099, 989989, 988889, 987789, 986689, 985589, 984489, 983389, 982289, 981189, 980089, 979979, 978879, 977779, 976679, 975579, 974479, 973379, 972279, 971179, 970079, 969969, 968869, 967769, 966669, 965569, 964469, 963369, 962269, 961169, 960069, 959959, 958859, 957759, 956659, 955559, 954459, 953359, 952259, 951159, 950059, 949949, 948849, 947749, 946649, 945549, 944449, 943349, 942249, 941149, 940049, 939939, 938839, 937739, 936639, 935539, 934439, 933339, 932239, 931139, 930039, 929929, 928829, 927729, 926629, 925529, 924429, 923329, 922229, 921129, 920029, 919919, 918819, 917719, 916619, 915519, 914419, 913319, 912219, 911119, 910019, 909909, 908809, 907709, 906609, 905509, 904409, 903309, 902209, 901109, 900009, 899998, 898898, 897798, 896698, 895598, 894498, 893398, 892298, 891198, 890098, 889988, 888888, 887788, 886688, 885588, 884488, 883388, 882288, 881188, 880088, 879978, 878878, 877778, 876678, 875578, 874478, 873378, 872278, 871178, 870078, 869968, 868868, 867768, 866668, 865568, 864468, 863368, 862268, 861168, 860068, 859958, 858858, 857758, 856658, 855558, 854458, 853358, 852258, 851158, 850058, 849948, 848848, 847748, 846648, 845548, 844448, 843348, 842248, 841148, 840048, 839938, 838838, 837738, 836638, 835538, 834438, 833338, 832238, 831138, 830038, 829928, 828828, 827728, 826628, 825528, 824428, 823328, 822228, 821128, 820028, 819918, 818818, 817718, 816618, 815518, 814418, 813318, 812218, 811118, 810018, 809908, 808808, 807708, 806608, 805508, 804408, 803308, 802208, 801108, 800008, 799997, 798897, 797797, 796697, 795597, 794497, 793397, 792297, 791197, 790097, 789987, 788887, 787787, 786687, 785587, 784487, 783387, 782287, 781187, 780087, 779977, 778877, 777777, 776677, 775577, 774477, 773377, 772277, 771177, 770077, 769967, 768867, 767767, 766667, 765567, 764467, 763367, 762267, 761167, 760067, 759957, 758857, 757757, 756657, 755557, 754457, 753357, 752257, 751157, 750057, 749947, 748847, 747747, 746647, 745547, 744447, 743347, 742247, 741147, 740047, 739937, 738837, 737737, 736637, 735537, 734437, 733337, 732237, 731137, 730037, 729927, 728827, 727727, 726627, 725527, 724427, 723327, 722227, 721127, 720027, 719917, 718817, 717717, 716617, 715517, 714417, 713317, 712217, 711117, 710017, 709907, 708807, 707707, 706607, 705507, 704407, 703307, 702207, 701107, 700007, 699996, 698896, 697796, 696696, 695596, 694496, 693396, 692296, 691196, 690096, 689986, 688886, 687786, 686686, 685586, 684486, 683386, 682286, 681186, 680086, 679976, 678876, 677776, 676676, 675576, 674476, 673376, 672276, 671176, 670076, 669966, 668866, 667766, 666666, 665566, 664466, 663366, 662266, 661166, 660066, 659956, 658856, 657756, 656656, 655556, 654456, 653356, 652256, 651156, 650056, 649946, 648846, 647746, 646646, 645546, 644446, 643346, 642246, 641146, 640046, 639936, 638836, 637736, 636636, 635536, 634436, 633336, 632236, 631136, 630036, 629926, 628826, 627726, 626626, 625526, 624426, 623326, 622226, 621126, 620026, 619916, 618816, 617716, 616616, 615516, 614416, 613316, 612216, 611116, 610016, 609906, 608806, 607706, 606606, 605506, 604406, 603306, 602206, 601106, 600006, 599995, 598895, 597795, 596695, 595595, 594495, 593395, 592295, 591195, 590095, 589985, 588885, 587785, 586685, 585585, 584485, 583385, 582285, 581185, 580085, 579975, 578875, 577775, 576675, 575575, 574475, 573375, 572275, 571175, 570075, 569965, 568865, 567765, 566665, 565565, 564465, 563365, 562265, 561165, 560065, 559955, 558855, 557755, 556655, 555555, 554455, 553355, 552255, 551155, 550055, 549945, 548845, 547745, 546645, 545545, 544445, 543345, 542245, 541145, 540045, 539935, 538835, 537735, 536635, 535535, 534435, 533335, 532235, 531135, 530035, 529925, 528825, 527725, 526625, 525525, 524425, 523325, 522225, 521125, 520025, 519915, 518815, 517715, 516615, 515515, 514415, 513315, 512215, 511115, 510015, 509905, 508805, 507705, 506605, 505505, 504405, 503305, 502205, 501105, 500005, 499994, 498894, 497794, 496694, 495594, 494494, 493394, 492294, 491194, 490094, 489984, 488884, 487784, 486684, 485584, 484484, 483384, 482284, 481184, 480084, 479974, 478874, 477774, 476674, 475574, 474474, 473374, 472274, 471174, 470074, 469964, 468864, 467764, 466664, 465564, 464464, 463364, 462264, 461164, 460064, 459954, 458854, 457754, 456654, 455554, 454454, 453354, 452254, 451154, 450054, 449944, 448844, 447744, 446644, 445544, 444444, 443344, 442244, 441144, 440044, 439934, 438834, 437734, 436634, 435534, 434434, 433334, 432234, 431134, 430034, 429924, 428824, 427724, 426624, 425524, 424424, 423324, 422224, 421124, 420024, 419914, 418814, 417714, 416614, 415514, 414414, 413314, 412214, 411114, 410014, 409904, 408804, 407704, 406604, 405504, 404404, 403304, 402204, 401104, 400004, 399993, 398893, 397793, 396693, 395593, 394493, 393393, 392293, 391193, 390093, 389983, 388883, 387783, 386683, 385583, 384483, 383383, 382283, 381183, 380083, 379973, 378873, 377773, 376673, 375573, 374473, 373373, 372273, 371173, 370073, 369963, 368863, 367763, 366663, 365563, 364463, 363363, 362263, 361163, 360063, 359953, 358853, 357753, 356653, 355553, 354453, 353353, 352253, 351153, 350053, 349943, 348843, 347743, 346643, 345543, 344443, 343343, 342243, 341143, 340043, 339933, 338833, 337733, 336633, 335533, 334433, 333333, 332233, 331133, 330033, 329923, 328823, 327723, 326623, 325523, 324423, 323323, 322223, 321123, 320023, 319913, 318813, 317713, 316613, 315513, 314413, 313313, 312213, 311113, 310013, 309903, 308803, 307703, 306603, 305503, 304403, 303303, 302203, 301103, 300003, 299992, 298892, 297792, 296692, 295592, 294492, 293392, 292292, 291192, 290092, 289982, 288882, 287782, 286682, 285582, 284482, 283382, 282282, 281182, 280082, 279972, 278872, 277772, 276672, 275572, 274472, 273372, 272272, 271172, 270072, 269962, 268862, 267762, 266662, 265562, 264462, 263362, 262262, 261162, 260062, 259952, 258852, 257752, 256652, 255552, 254452, 253352, 252252, 251152, 250052, 249942, 248842, 247742, 246642, 245542, 244442, 243342, 242242, 241142, 240042, 239932, 238832, 237732, 236632, 235532, 234432, 233332, 232232, 231132, 230032, 229922, 228822, 227722, 226622, 225522, 224422, 223322, 222222, 221122, 220022, 219912, 218812, 217712, 216612, 215512, 214412, 213312, 212212, 211112, 210012, 209902, 208802, 207702, 206602, 205502, 204402, 203302, 202202, 201102, 200002, 199991, 198891, 197791, 196691, 195591, 194491, 193391, 192291, 191191, 190091, 189981, 188881, 187781, 186681, 185581, 184481, 183381, 182281, 181181, 180081, 179971, 178871, 177771, 176671, 175571, 174471, 173371, 172271, 171171, 170071, 169961, 168861, 167761, 166661, 165561, 164461, 163361, 162261, 161161, 160061, 159951, 158851, 157751, 156651, 155551, 154451, 153351, 152251, 151151, 150051, 149941, 148841, 147741, 146641, 145541, 144441, 143341, 142241, 141141, 140041, 139931, 138831, 137731, 136631, 135531, 134431, 133331, 132231, 131131, 130031, 129921, 128821, 127721, 126621, 125521, 124421, 123321, 122221, 121121, 120021, 119911, 118811, 117711, 116611, 115511, 114411, 113311, 112211, 111111, 110011, 109901, 108801, 107701, 106601, 105501, 104401, 103301, 102201, 101101, 100001, 99999, 99899, 99799, 99699, 99599, 99499, 99399, 99299, 99199, 99099, 98989, 98889, 98789, 98689, 98589, 98489, 98389, 98289, 98189, 98089, 97979, 97879, 97779, 97679, 97579, 97479, 97379, 97279, 97179, 97079, 96969, 96869, 96769, 96669, 96569, 96469, 96369, 96269, 96169, 96069, 95959, 95859, 95759, 95659, 95559, 95459, 95359, 95259, 95159, 95059, 94949, 94849, 94749, 94649, 94549, 94449, 94349, 94249, 94149, 94049, 93939, 93839, 93739, 93639, 93539, 93439, 93339, 93239, 93139, 93039, 92929, 92829, 92729, 92629, 92529, 92429, 92329, 92229, 92129, 92029, 91919, 91819, 91719, 91619, 91519, 91419, 91319, 91219, 91119, 91019, 90909, 90809, 90709, 90609, 90509, 90409, 90309, 90209, 90109, 90009, 89998, 89898, 89798, 89698, 89598, 89498, 89398, 89298, 89198, 89098, 88988, 88888, 88788, 88688, 88588, 88488, 88388, 88288, 88188, 88088, 87978, 87878, 87778, 87678, 87578, 87478, 87378, 87278, 87178, 87078, 86968, 86868, 86768, 86668, 86568, 86468, 86368, 86268, 86168, 86068, 85958, 85858, 85758, 85658, 85558, 85458, 85358, 85258, 85158, 85058, 84948, 84848, 84748, 84648, 84548, 84448, 84348, 84248, 84148, 84048, 83938, 83838, 83738, 83638, 83538, 83438, 83338, 83238, 83138, 83038, 82928, 82828, 82728, 82628, 82528, 82428, 82328, 82228, 82128, 82028, 81918, 81818, 81718, 81618, 81518, 81418, 81318, 81218, 81118, 81018, 80908, 80808, 80708, 80608, 80508, 80408, 80308, 80208, 80108, 80008, 79997, 79897, 79797, 79697, 79597, 79497, 79397, 79297, 79197, 79097, 78987, 78887, 78787, 78687, 78587, 78487, 78387, 78287, 78187, 78087, 77977, 77877, 77777, 77677, 77577, 77477, 77377, 77277, 77177, 77077, 76967, 76867, 76767, 76667, 76567, 76467, 76367, 76267, 76167, 76067, 75957, 75857, 75757, 75657, 75557, 75457, 75357, 75257, 75157, 75057, 74947, 74847, 74747, 74647, 74547, 74447, 74347, 74247, 74147, 74047, 73937, 73837, 73737, 73637, 73537, 73437, 73337, 73237, 73137, 73037, 72927, 72827, 72727, 72627, 72527, 72427, 72327, 72227, 72127, 72027, 71917, 71817, 71717, 71617, 71517, 71417, 71317, 71217, 71117, 71017, 70907, 70807, 70707, 70607, 70507, 70407, 70307, 70207, 70107, 70007, 69996, 69896, 69796, 69696, 69596, 69496, 69396, 69296, 69196, 69096, 68986, 68886, 68786, 68686, 68586, 68486, 68386, 68286, 68186, 68086, 67976, 67876, 67776, 67676, 67576, 67476, 67376, 67276, 67176, 67076, 66966, 66866, 66766, 66666, 66566, 66466, 66366, 66266, 66166, 66066, 65956, 65856, 65756, 65656, 65556, 65456, 65356, 65256, 65156, 65056, 64946, 64846, 64746, 64646, 64546, 64446, 64346, 64246, 64146, 64046, 63936, 63836, 63736, 63636, 63536, 63436, 63336, 63236, 63136, 63036, 62926, 62826, 62726, 62626, 62526, 62426, 62326, 62226, 62126, 62026, 61916, 61816, 61716, 61616, 61516, 61416, 61316, 61216, 61116, 61016, 60906, 60806, 60706, 60606, 60506, 60406, 60306, 60206, 60106, 60006, 59995, 59895, 59795, 59695, 59595, 59495, 59395, 59295, 59195, 59095, 58985, 58885, 58785, 58685, 58585, 58485, 58385, 58285, 58185, 58085, 57975, 57875, 57775, 57675, 57575, 57475, 57375, 57275, 57175, 57075, 56965, 56865, 56765, 56665, 56565, 56465, 56365, 56265, 56165, 56065, 55955, 55855, 55755, 55655, 55555, 55455, 55355, 55255, 55155, 55055, 54945, 54845, 54745, 54645, 54545, 54445, 54345, 54245, 54145, 54045, 53935, 53835, 53735, 53635, 53535, 53435, 53335, 53235, 53135, 53035, 52925, 52825, 52725, 52625, 52525, 52425, 52325, 52225, 52125, 52025, 51915, 51815, 51715, 51615, 51515, 51415, 51315, 51215, 51115, 51015, 50905, 50805, 50705, 50605, 50505, 50405, 50305, 50205, 50105, 50005, 49994, 49894, 49794, 49694, 49594, 49494, 49394, 49294, 49194, 49094, 48984, 48884, 48784, 48684, 48584, 48484, 48384, 48284, 48184, 48084, 47974, 47874, 47774, 47674, 47574, 47474, 47374, 47274, 47174, 47074, 46964, 46864, 46764, 46664, 46564, 46464, 46364, 46264, 46164, 46064, 45954, 45854, 45754, 45654, 45554, 45454, 45354, 45254, 45154, 45054, 44944, 44844, 44744, 44644, 44544, 44444, 44344, 44244, 44144, 44044, 43934, 43834, 43734, 43634, 43534, 43434, 43334, 43234, 43134, 43034, 42924, 42824, 42724, 42624, 42524, 42424, 42324, 42224, 42124, 42024, 41914, 41814, 41714, 41614, 41514, 41414, 41314, 41214, 41114, 41014, 40904, 40804, 40704, 40604, 40504, 40404, 40304, 40204, 40104, 40004, 39993, 39893, 39793, 39693, 39593, 39493, 39393, 39293, 39193, 39093, 38983, 38883, 38783, 38683, 38583, 38483, 38383, 38283, 38183, 38083, 37973, 37873, 37773, 37673, 37573, 37473, 37373, 37273, 37173, 37073, 36963, 36863, 36763, 36663, 36563, 36463, 36363, 36263, 36163, 36063, 35953, 35853, 35753, 35653, 35553, 35453, 35353, 35253, 35153, 35053, 34943, 34843, 34743, 34643, 34543, 34443, 34343, 34243, 34143, 34043, 33933, 33833, 33733, 33633, 33533, 33433, 33333, 33233, 33133, 33033, 32923, 32823, 32723, 32623, 32523, 32423, 32323, 32223, 32123, 32023, 31913, 31813, 31713, 31613, 31513, 31413, 31313, 31213, 31113, 31013, 30903, 30803, 30703, 30603, 30503, 30403, 30303, 30203, 30103, 30003, 29992, 29892, 29792, 29692, 29592, 29492, 29392, 29292, 29192, 29092, 28982, 28882, 28782, 28682, 28582, 28482, 28382, 28282, 28182, 28082, 27972, 27872, 27772, 27672, 27572, 27472, 27372, 27272, 27172, 27072, 26962, 26862, 26762, 26662, 26562, 26462, 26362, 26262, 26162, 26062, 25952, 25852, 25752, 25652, 25552, 25452, 25352, 25252, 25152, 25052, 24942, 24842, 24742, 24642, 24542, 24442, 24342, 24242, 24142, 24042, 23932, 23832, 23732, 23632, 23532, 23432, 23332, 23232, 23132, 23032, 22922, 22822, 22722, 22622, 22522, 22422, 22322, 22222, 22122, 22022, 21912, 21812, 21712, 21612, 21512, 21412, 21312, 21212, 21112, 21012, 20902, 20802, 20702, 20602, 20502, 20402, 20302, 20202, 20102, 20002, 19991, 19891, 19791, 19691, 19591, 19491, 19391, 19291, 19191, 19091, 18981, 18881, 18781, 18681, 18581, 18481, 18381, 18281, 18181, 18081, 17971, 17871, 17771, 17671, 17571, 17471, 17371, 17271, 17171, 17071, 16961, 16861, 16761, 16661, 16561, 16461, 16361, 16261, 16161, 16061, 15951, 15851, 15751, 15651, 15551, 15451, 15351, 15251, 15151, 15051, 14941, 14841, 14741, 14641, 14541, 14441, 14341, 14241, 14141, 14041, 13931, 13831, 13731, 13631, 13531, 13431, 13331, 13231, 13131, 13031, 12921, 12821, 12721, 12621, 12521, 12421, 12321, 12221, 12121, 12021, 11911, 11811, 11711, 11611, 11511, 11411, 11311, 11211, 11111, 11011, 10901, 10801, 10701, 10601, 10501, 10401, 10301, 10201, 10101, 10001}
set pal_set_ref to a reference to pal_set
set div_set to {999, 998, 997, 996, 995, 994, 993, 992, 991, 989, 988, 987, 986, 985, 984, 983, 982, 981, 979, 978, 977, 976, 975, 974, 973, 972, 971, 969, 968, 967, 966, 965, 964, 963, 962, 961, 959, 958, 957, 956, 955, 954, 953, 952, 951, 949, 948, 947, 946, 945, 944, 943, 942, 941, 939, 938, 937, 936, 935, 934, 933, 932, 931, 929, 928, 927, 926, 925, 924, 923, 922, 921, 919, 918, 917, 916, 915, 914, 913, 912, 911, 909, 908, 907, 906, 905, 904, 903, 902, 901, 899, 898, 897, 896, 895, 894, 893, 892, 891, 889, 888, 887, 886, 885, 884, 883, 882, 881, 879, 878, 877, 876, 875, 874, 873, 872, 871, 869, 868, 867, 866, 865, 864, 863, 862, 861, 859, 858, 857, 856, 855, 854, 853, 852, 851, 849, 848, 847, 846, 845, 844, 843, 842, 841, 839, 838, 837, 836, 835, 834, 833, 832, 831, 829, 828, 827, 826, 825, 824, 823, 822, 821, 819, 818, 817, 816, 815, 814, 813, 812, 811, 809, 808, 807, 806, 805, 804, 803, 802, 801, 799, 798, 797, 796, 795, 794, 793, 792, 791, 789, 788, 787, 786, 785, 784, 783, 782, 781, 779, 778, 777, 776, 775, 774, 773, 772, 771, 769, 768, 767, 766, 765, 764, 763, 762, 761, 759, 758, 757, 756, 755, 754, 753, 752, 751, 749, 748, 747, 746, 745, 744, 743, 742, 741, 739, 738, 737, 736, 735, 734, 733, 732, 731, 729, 728, 727, 726, 725, 724, 723, 722, 721, 719, 718, 717, 716, 715, 714, 713, 712, 711, 709, 708, 707, 706, 705, 704, 703, 702, 701, 699, 698, 697, 696, 695, 694, 693, 692, 691, 689, 688, 687, 686, 685, 684, 683, 682, 681, 679, 678, 677, 676, 675, 674, 673, 672, 671, 669, 668, 667, 666, 665, 664, 663, 662, 661, 659, 658, 657, 656, 655, 654, 653, 652, 651, 649, 648, 647, 646, 645, 644, 643, 642, 641, 639, 638, 637, 636, 635, 634, 633, 632, 631, 629, 628, 627, 626, 625, 624, 623, 622, 621, 619, 618, 617, 616, 615, 614, 613, 612, 611, 609, 608, 607, 606, 605, 604, 603, 602, 601, 599, 598, 597, 596, 595, 594, 593, 592, 591, 589, 588, 587, 586, 585, 584, 583, 582, 581, 579, 578, 577, 576, 575, 574, 573, 572, 571, 569, 568, 567, 566, 565, 564, 563, 562, 561, 559, 558, 557, 556, 555, 554, 553, 552, 551, 549, 548, 547, 546, 545, 544, 543, 542, 541, 539, 538, 537, 536, 535, 534, 533, 532, 531, 529, 528, 527, 526, 525, 524, 523, 522, 521, 519, 518, 517, 516, 515, 514, 513, 512, 511, 509, 508, 507, 506, 505, 504, 503, 502, 501, 499, 498, 497, 496, 495, 494, 493, 492, 491, 489, 488, 487, 486, 485, 484, 483, 482, 481, 479, 478, 477, 476, 475, 474, 473, 472, 471, 469, 468, 467, 466, 465, 464, 463, 462, 461, 459, 458, 457, 456, 455, 454, 453, 452, 451, 449, 448, 447, 446, 445, 444, 443, 442, 441, 439, 438, 437, 436, 435, 434, 433, 432, 431, 429, 428, 427, 426, 425, 424, 423, 422, 421, 419, 418, 417, 416, 415, 414, 413, 412, 411, 409, 408, 407, 406, 405, 404, 403, 402, 401, 399, 398, 397, 396, 395, 394, 393, 392, 391, 389, 388, 387, 386, 385, 384, 383, 382, 381, 379, 378, 377, 376, 375, 374, 373, 372, 371, 369, 368, 367, 366, 365, 364, 363, 362, 361, 359, 358, 357, 356, 355, 354, 353, 352, 351, 349, 348, 347, 346, 345, 344, 343, 342, 341, 339, 338, 337, 336, 335, 334, 333, 332, 331, 329, 328, 327, 326, 325, 324, 323, 322, 321, 319, 318, 317, 316, 315, 314, 313, 312, 311, 309, 308, 307, 306, 305, 304, 303, 302, 301, 299, 298, 297, 296, 295, 294, 293, 292, 291, 289, 288, 287, 286, 285, 284, 283, 282, 281, 279, 278, 277, 276, 275, 274, 273, 272, 271, 269, 268, 267, 266, 265, 264, 263, 262, 261, 259, 258, 257, 256, 255, 254, 253, 252, 251, 249, 248, 247, 246, 245, 244, 243, 242, 241, 239, 238, 237, 236, 235, 234, 233, 232, 231, 229, 228, 227, 226, 225, 224, 223, 222, 221, 219, 218, 217, 216, 215, 214, 213, 212, 211, 209, 208, 207, 206, 205, 204, 203, 202, 201, 199, 198, 197, 196, 195, 194, 193, 192, 191, 189, 188, 187, 186, 185, 184, 183, 182, 181, 179, 178, 177, 176, 175, 174, 173, 172, 171, 169, 168, 167, 166, 165, 164, 163, 162, 161, 159, 158, 157, 156, 155, 154, 153, 152, 151, 149, 148, 147, 146, 145, 144, 143, 142, 141, 139, 138, 137, 136, 135, 134, 133, 132, 131, 129, 128, 127, 126, 125, 124, 123, 122, 121, 119, 118, 117, 116, 115, 114, 113, 112, 111, 109, 108, 107, 106, 105, 104, 103, 102, 101}
set div_set_ref to a reference to div_set
repeat with i in pal_set_ref
repeat with j in div_set_ref
set k to i / j
if (k mod 1 is 0) and (k < 1000) then log {i, j, (i / j)}
end repeat
end repeat