yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1092677	1092677	[ "1092677 1092677 1" ]
1116349	13 79 1087	[ "1116349 13 85873", "85873 79 1087", "1087 1087 1" ]
4058842	2 947 2143	[ "4058842 2 2029421", "2029421 947 2143", "2143 2143 1" ]
3109387	3109387	[ "3109387 3109387 1" ]
4637965	5 151 6143	[ "4637965 5 927593", "927593 151 6143", "6143 6143 1" ]
1642564	2 2 7 11 5333	[ "1642564 2 821282", "821282 2 410641", "410641 7 58663", "58663 11 5333", "5333 5333 1" ]
1223765	5 244753	[ "1223765 5 244753", "244753 244753 1" ]
1529759	7 11 19867	[ "1529759 7 218537", "218537 11 19867", "19867 19867 1" ]
1931971	103 18757	[ "1931971 103 18757", "18757 18757 1" ]
3326655	3 5 463 479	[ "3326655 3 1108885", "1108885 5 221777", "221777 463 479", "479 479 1" ]
3465389	3465389	[ "3465389 3465389 1" ]
3034953	3 3 337217	[ "3034953 3 1011651", "1011651 3 337217", "337217 337217 1" ]
4963681	71 69911	[ "4963681 71 69911", "69911 69911 1" ]
2604163	2604163	[ "2604163 2604163 1" ]
1813188	2 2 3 13 59 197	[ "1813188 2 906594", "906594 2 453297", "453297 3 151099", "151099 13 11623", "11623 59 197", "197 197 1" ]
927461	41 22621	[ "927461 41 22621", "22621 22621 1" ]
4587808	2 2 2 2 2 307 467	[ "4587808 2 2293904", "2293904 2 1146952", "1146952 2 573476", "573476 2 286738", "286738 2 143369", "143369 307 467", "467 467 1" ]
2176493	11 17 103 113	[ "2176493 11 197863", "197863 17 11639", "11639 103 113", "113 113 1" ]
4873205	5 683 1427	[ "4873205 5 974641", "974641 683 1427", "1427 1427 1" ]
2757591	3 3 3 109 937	[ "2757591 3 919197", "919197 3 306399", "306399 3 102133", "102133 109 937", "937 937 1" ]
1280967	3 17 25117	[ "1280967 3 426989", "426989 17 25117", "25117 25117 1" ]
4944518	2 17 41 3547	[ "4944518 2 2472259", "2472259 17 145427", "145427 41 3547", "3547 3547 1" ]
935969	17 55057	[ "935969 17 55057", "55057 55057 1" ]
4938249	3 43 38281	[ "4938249 3 1646083", "1646083 43 38281", "38281 38281 1" ]
2122952	2 2 2 13 137 149	[ "2122952 2 1061476", "1061476 2 530738", "530738 2 265369", "265369 13 20413", "20413 137 149", "149 149 1" ]
3303178	2 1651589	[ "3303178 2 1651589", "1651589 1651589 1" ]
417181	417181	[ "417181 417181 1" ]
1167160	2 2 2 5 29179	[ "1167160 2 583580", "583580 2 291790", "291790 2 145895", "145895 5 29179", "29179 29179 1" ]
3233578	2 37 37 1181	[ "3233578 2 1616789", "1616789 37 43697", "43697 37 1181", "1181 1181 1" ]
2366558	2 1183279	[ "2366558 2 1183279", "1183279 1183279 1" ]
3102207	3 1034069	[ "3102207 3 1034069", "1034069 1034069 1" ]
172062	2 3 3 11 11 79	[ "172062 2 86031", "86031 3 28677", "28677 3 9559", "9559 11 869", "869 11 79", "79 79 1" ]
57535	5 37 311	[ "57535 5 11507", "11507 37 311", "311 311 1" ]
4071627	3 3 3 3 7 43 167	[ "4071627 3 1357209", "1357209 3 452403", "452403 3 150801", "150801 3 50267", "50267 7 7181", "7181 43 167", "167 167 1" ]
2807975	5 5 17 6607	[ "2807975 5 561595", "561595 5 112319", "112319 17 6607", "6607 6607 1" ]
4628072	2 2 2 578509	[ "4628072 2 2314036", "2314036 2 1157018", "1157018 2 578509", "578509 578509 1" ]
4219707	3 47 29927	[ "4219707 3 1406569", "1406569 47 29927", "29927 29927 1" ]
54966	2 3 9161	[ "54966 2 27483", "27483 3 9161", "9161 9161 1" ]
519781	61 8521	[ "519781 61 8521", "8521 8521 1" ]
3243889	11 11 17 19 83	[ "3243889 11 294899", "294899 11 26809", "26809 17 1577", "1577 19 83", "83 83 1" ]
2499164	2 2 624791	[ "2499164 2 1249582", "1249582 2 624791", "624791 624791 1" ]
1491455	5 7 43 991	[ "1491455 5 298291", "298291 7 42613", "42613 43 991", "991 991 1" ]
2463247	107 23021	[ "2463247 107 23021", "23021 23021 1" ]
314629	7 7 6421	[ "314629 7 44947", "44947 7 6421", "6421 6421 1" ]
4518402	2 3 7 107581	[ "4518402 2 2259201", "2259201 3 753067", "753067 7 107581", "107581 107581 1" ]
4199638	2 43 47 1039	[ "4199638 2 2099819", "2099819 43 48833", "48833 47 1039", "1039 1039 1" ]
2464512	2 2 2 2 2 2 2 2 3 3209	[ "2464512 2 1232256", "1232256 2 616128", "616128 2 308064", "308064 2 154032", "154032 2 77016", "77016 2 38508", "38508 2 19254", "19254 2 9627", "9627 3 3209", "3209 3209 1" ]
4515584	2 2 2 2 2 2 2 2 31 569	[ "4515584 2 2257792", "2257792 2 1128896", "1128896 2 564448", "564448 2 282224", "282224 2 141112", "141112 2 70556", "70556 2 35278", "35278 2 17639", "17639 31 569", "569 569 1" ]
484306	2 103 2351	[ "484306 2 242153", "242153 103 2351", "2351 2351 1" ]
4237521	3 43 107 307	[ "4237521 3 1412507", "1412507 43 32849", "32849 107 307", "307 307 1" ]
4236299	431 9829	[ "4236299 431 9829", "9829 9829 1" ]
4943642	2 11 224711	[ "4943642 2 2471821", "2471821 11 224711", "224711 224711 1" ]
3118563	3 3 7 59 839	[ "3118563 3 1039521", "1039521 3 346507", "346507 7 49501", "49501 59 839", "839 839 1" ]
4318201	4318201	[ "4318201 4318201 1" ]
2175682	2 1087841	[ "2175682 2 1087841", "1087841 1087841 1" ]
2956027	251 11777	[ "2956027 251 11777", "11777 11777 1" ]
2518343	41 239 257	[ "2518343 41 61423", "61423 239 257", "257 257 1" ]
559923	3 7 7 13 293	[ "559923 3 186641", "186641 7 26663", "26663 7 3809", "3809 13 293", "293 293 1" ]
3087855	3 3 3 5 89 257	[ "3087855 3 1029285", "1029285 3 343095", "343095 3 114365", "114365 5 22873", "22873 89 257", "257 257 1" ]
3944046	2 3 43 15287	[ "3944046 2 1972023", "1972023 3 657341", "657341 43 15287", "15287 15287 1" ]
4594782	2 3 53 14449	[ "4594782 2 2297391", "2297391 3 765797", "765797 53 14449", "14449 14449 1" ]
3050362	2 7 53 4111	[ "3050362 2 1525181", "1525181 7 217883", "217883 53 4111", "4111 4111 1" ]
4623686	2 2311843	[ "4623686 2 2311843", "2311843 2311843 1" ]
4509880	2 2 2 5 31 3637	[ "4509880 2 2254940", "2254940 2 1127470", "1127470 2 563735", "563735 5 112747", "112747 31 3637", "3637 3637 1" ]
4806820	2 2 5 240341	[ "4806820 2 2403410", "2403410 2 1201705", "1201705 5 240341", "240341 240341 1" ]
2916930	2 3 5 97231	[ "2916930 2 1458465", "1458465 3 486155", "486155 5 97231", "97231 97231 1" ]
763537	61 12517	[ "763537 61 12517", "12517 12517 1" ]
2039060	2 2 5 43 2371	[ "2039060 2 1019530", "1019530 2 509765", "509765 5 101953", "101953 43 2371", "2371 2371 1" ]
4296647	4296647	[ "4296647 4296647 1" ]
268018	2 29 4621	[ "268018 2 134009", "134009 29 4621", "4621 4621 1" ]
3920838	2 3 653473	[ "3920838 2 1960419", "1960419 3 653473", "653473 653473 1" ]
1474063	733 2011	[ "1474063 733 2011", "2011 2011 1" ]
2557264	2 2 2 2 277 577	[ "2557264 2 1278632", "1278632 2 639316", "639316 2 319658", "319658 2 159829", "159829 277 577", "577 577 1" ]
2627231	17 154543	[ "2627231 17 154543", "154543 154543 1" ]
802978	2 11 17 19 113	[ "802978 2 401489", "401489 11 36499", "36499 17 2147", "2147 19 113", "113 113 1" ]
4873881	3 1624627	[ "4873881 3 1624627", "1624627 1624627 1" ]
3948291	3 3 3 257 569	[ "3948291 3 1316097", "1316097 3 438699", "438699 3 146233", "146233 257 569", "569 569 1" ]
4615006	2 11 89 2357	[ "4615006 2 2307503", "2307503 11 209773", "209773 89 2357", "2357 2357 1" ]
2989950	2 3 5 5 31 643	[ "2989950 2 1494975", "1494975 3 498325", "498325 5 99665", "99665 5 19933", "19933 31 643", "643 643 1" ]
949144	2 2 2 7 17 997	[ "949144 2 474572", "474572 2 237286", "237286 2 118643", "118643 7 16949", "16949 17 997", "997 997 1" ]
2960159	17 31 41 137	[ "2960159 17 174127", "174127 31 5617", "5617 41 137", "137 137 1" ]
962525	5 5 38501	[ "962525 5 192505", "192505 5 38501", "38501 38501 1" ]
601762	2 7 53 811	[ "601762 2 300881", "300881 7 42983", "42983 53 811", "811 811 1" ]
3636983	7 43 43 281	[ "3636983 7 519569", "519569 43 12083", "12083 43 281", "281 281 1" ]
4674788	2 2 43 27179	[ "4674788 2 2337394", "2337394 2 1168697", "1168697 43 27179", "27179 27179 1" ]
2564868	2 2 3 23 9293	[ "2564868 2 1282434", "1282434 2 641217", "641217 3 213739", "213739 23 9293", "9293 9293 1" ]
4978088	2 2 2 61 101 101	[ "4978088 2 2489044", "2489044 2 1244522", "1244522 2 622261", "622261 61 10201", "10201 101 101", "101 101 1" ]
4019268	2 2 3 11 30449	[ "4019268 2 2009634", "2009634 2 1004817", "1004817 3 334939", "334939 11 30449", "30449 30449 1" ]
3879698	2 173 11213	[ "3879698 2 1939849", "1939849 173 11213", "11213 11213 1" ]
4960375	5 5 5 7 5669	[ "4960375 5 992075", "992075 5 198415", "198415 5 39683", "39683 7 5669", "5669 5669 1" ]
3006308	2 2 47 15991	[ "3006308 2 1503154", "1503154 2 751577", "751577 47 15991", "15991 15991 1" ]
1614895	5 71 4549	[ "1614895 5 322979", "322979 71 4549", "4549 4549 1" ]
3537361	47 73 1031	[ "3537361 47 75263", "75263 73 1031", "1031 1031 1" ]
2350018	2 11 37 2887	[ "2350018 2 1175009", "1175009 11 106819", "106819 37 2887", "2887 2887 1" ]
4676255	5 41 22811	[ "4676255 5 935251", "935251 41 22811", "22811 22811 1" ]
3164917	7 452131	[ "3164917 7 452131", "452131 452131 1" ]
1866636	2 2 3 3 19 2729	[ "1866636 2 933318", "933318 2 466659", "466659 3 155553", "155553 3 51851", "51851 19 2729", "2729 2729 1" ]
1479304	2 2 2 184913	[ "1479304 2 739652", "739652 2 369826", "369826 2 184913", "184913 184913 1" ]
2070773	47 44059	[ "2070773 47 44059", "44059 44059 1" ]
3567743	89 40087	[ "3567743 89 40087", "40087 40087 1" ]

1092677

[ "1092677 1092677 1" ]

1116349

13 79 1087

[ "1116349 13 85873", "85873 79 1087", "1087 1087 1" ]

4058842

2 947 2143

[ "4058842 2 2029421", "2029421 947 2143", "2143 2143 1" ]

3109387

[ "3109387 3109387 1" ]

4637965

5 151 6143

[ "4637965 5 927593", "927593 151 6143", "6143 6143 1" ]

1642564

2 2 7 11 5333

[ "1642564 2 821282", "821282 2 410641", "410641 7 58663", "58663 11 5333", "5333 5333 1" ]

1223765

5 244753

[ "1223765 5 244753", "244753 244753 1" ]

1529759

7 11 19867

[ "1529759 7 218537", "218537 11 19867", "19867 19867 1" ]

1931971

103 18757

[ "1931971 103 18757", "18757 18757 1" ]

3326655

3 5 463 479

[ "3326655 3 1108885", "1108885 5 221777", "221777 463 479", "479 479 1" ]

3465389

[ "3465389 3465389 1" ]

3034953

3 3 337217

[ "3034953 3 1011651", "1011651 3 337217", "337217 337217 1" ]

4963681

71 69911

[ "4963681 71 69911", "69911 69911 1" ]

2604163

[ "2604163 2604163 1" ]

1813188

2 2 3 13 59 197

[ "1813188 2 906594", "906594 2 453297", "453297 3 151099", "151099 13 11623", "11623 59 197", "197 197 1" ]

927461

41 22621

[ "927461 41 22621", "22621 22621 1" ]

4587808

2 2 2 2 2 307 467

[ "4587808 2 2293904", "2293904 2 1146952", "1146952 2 573476", "573476 2 286738", "286738 2 143369", "143369 307 467", "467 467 1" ]

2176493

11 17 103 113

[ "2176493 11 197863", "197863 17 11639", "11639 103 113", "113 113 1" ]

4873205

5 683 1427

[ "4873205 5 974641", "974641 683 1427", "1427 1427 1" ]

2757591

3 3 3 109 937

[ "2757591 3 919197", "919197 3 306399", "306399 3 102133", "102133 109 937", "937 937 1" ]

1280967

3 17 25117

[ "1280967 3 426989", "426989 17 25117", "25117 25117 1" ]

4944518

2 17 41 3547

[ "4944518 2 2472259", "2472259 17 145427", "145427 41 3547", "3547 3547 1" ]

935969

17 55057

[ "935969 17 55057", "55057 55057 1" ]

4938249

3 43 38281

[ "4938249 3 1646083", "1646083 43 38281", "38281 38281 1" ]

2122952

2 2 2 13 137 149

[ "2122952 2 1061476", "1061476 2 530738", "530738 2 265369", "265369 13 20413", "20413 137 149", "149 149 1" ]

3303178

2 1651589

[ "3303178 2 1651589", "1651589 1651589 1" ]

417181

[ "417181 417181 1" ]

1167160

2 2 2 5 29179

[ "1167160 2 583580", "583580 2 291790", "291790 2 145895", "145895 5 29179", "29179 29179 1" ]

3233578

2 37 37 1181

[ "3233578 2 1616789", "1616789 37 43697", "43697 37 1181", "1181 1181 1" ]

2366558

2 1183279

[ "2366558 2 1183279", "1183279 1183279 1" ]

3102207

3 1034069

[ "3102207 3 1034069", "1034069 1034069 1" ]

172062

2 3 3 11 11 79

[ "172062 2 86031", "86031 3 28677", "28677 3 9559", "9559 11 869", "869 11 79", "79 79 1" ]

57535

5 37 311

[ "57535 5 11507", "11507 37 311", "311 311 1" ]

4071627

3 3 3 3 7 43 167

[ "4071627 3 1357209", "1357209 3 452403", "452403 3 150801", "150801 3 50267", "50267 7 7181", "7181 43 167", "167 167 1" ]

2807975

5 5 17 6607

[ "2807975 5 561595", "561595 5 112319", "112319 17 6607", "6607 6607 1" ]

4628072

2 2 2 578509

[ "4628072 2 2314036", "2314036 2 1157018", "1157018 2 578509", "578509 578509 1" ]

4219707

3 47 29927

[ "4219707 3 1406569", "1406569 47 29927", "29927 29927 1" ]

54966

2 3 9161

[ "54966 2 27483", "27483 3 9161", "9161 9161 1" ]

519781

61 8521

[ "519781 61 8521", "8521 8521 1" ]

3243889

11 11 17 19 83

[ "3243889 11 294899", "294899 11 26809", "26809 17 1577", "1577 19 83", "83 83 1" ]

2499164

2 2 624791

[ "2499164 2 1249582", "1249582 2 624791", "624791 624791 1" ]

1491455

5 7 43 991

[ "1491455 5 298291", "298291 7 42613", "42613 43 991", "991 991 1" ]

2463247

107 23021

[ "2463247 107 23021", "23021 23021 1" ]

314629

7 7 6421

[ "314629 7 44947", "44947 7 6421", "6421 6421 1" ]

4518402

2 3 7 107581

[ "4518402 2 2259201", "2259201 3 753067", "753067 7 107581", "107581 107581 1" ]

4199638

2 43 47 1039

[ "4199638 2 2099819", "2099819 43 48833", "48833 47 1039", "1039 1039 1" ]

2464512

2 2 2 2 2 2 2 2 3 3209

[ "2464512 2 1232256", "1232256 2 616128", "616128 2 308064", "308064 2 154032", "154032 2 77016", "77016 2 38508", "38508 2 19254", "19254 2 9627", "9627 3 3209", "3209 3209 1" ]

4515584

2 2 2 2 2 2 2 2 31 569

[ "4515584 2 2257792", "2257792 2 1128896", "1128896 2 564448", "564448 2 282224", "282224 2 141112", "141112 2 70556", "70556 2 35278", "35278 2 17639", "17639 31 569", "569 569 1" ]

484306

2 103 2351

[ "484306 2 242153", "242153 103 2351", "2351 2351 1" ]

4237521

3 43 107 307

[ "4237521 3 1412507", "1412507 43 32849", "32849 107 307", "307 307 1" ]

4236299

431 9829

[ "4236299 431 9829", "9829 9829 1" ]

4943642

2 11 224711

[ "4943642 2 2471821", "2471821 11 224711", "224711 224711 1" ]

3118563

3 3 7 59 839

[ "3118563 3 1039521", "1039521 3 346507", "346507 7 49501", "49501 59 839", "839 839 1" ]

4318201

[ "4318201 4318201 1" ]

2175682

2 1087841

[ "2175682 2 1087841", "1087841 1087841 1" ]

2956027

251 11777

[ "2956027 251 11777", "11777 11777 1" ]

2518343

41 239 257

[ "2518343 41 61423", "61423 239 257", "257 257 1" ]

559923

3 7 7 13 293

[ "559923 3 186641", "186641 7 26663", "26663 7 3809", "3809 13 293", "293 293 1" ]

3087855

3 3 3 5 89 257

[ "3087855 3 1029285", "1029285 3 343095", "343095 3 114365", "114365 5 22873", "22873 89 257", "257 257 1" ]

3944046

2 3 43 15287

[ "3944046 2 1972023", "1972023 3 657341", "657341 43 15287", "15287 15287 1" ]

4594782

2 3 53 14449

[ "4594782 2 2297391", "2297391 3 765797", "765797 53 14449", "14449 14449 1" ]

3050362

2 7 53 4111

[ "3050362 2 1525181", "1525181 7 217883", "217883 53 4111", "4111 4111 1" ]

4623686

2 2311843

[ "4623686 2 2311843", "2311843 2311843 1" ]

4509880

2 2 2 5 31 3637

[ "4509880 2 2254940", "2254940 2 1127470", "1127470 2 563735", "563735 5 112747", "112747 31 3637", "3637 3637 1" ]

4806820

2 2 5 240341

[ "4806820 2 2403410", "2403410 2 1201705", "1201705 5 240341", "240341 240341 1" ]

2916930

2 3 5 97231

[ "2916930 2 1458465", "1458465 3 486155", "486155 5 97231", "97231 97231 1" ]

763537

61 12517

[ "763537 61 12517", "12517 12517 1" ]

2039060

2 2 5 43 2371

[ "2039060 2 1019530", "1019530 2 509765", "509765 5 101953", "101953 43 2371", "2371 2371 1" ]

4296647

[ "4296647 4296647 1" ]

268018

2 29 4621

[ "268018 2 134009", "134009 29 4621", "4621 4621 1" ]

3920838

2 3 653473

[ "3920838 2 1960419", "1960419 3 653473", "653473 653473 1" ]

1474063

733 2011

[ "1474063 733 2011", "2011 2011 1" ]

2557264

2 2 2 2 277 577

[ "2557264 2 1278632", "1278632 2 639316", "639316 2 319658", "319658 2 159829", "159829 277 577", "577 577 1" ]

2627231

17 154543

[ "2627231 17 154543", "154543 154543 1" ]

802978

2 11 17 19 113

[ "802978 2 401489", "401489 11 36499", "36499 17 2147", "2147 19 113", "113 113 1" ]

4873881

3 1624627

[ "4873881 3 1624627", "1624627 1624627 1" ]

3948291

3 3 3 257 569

[ "3948291 3 1316097", "1316097 3 438699", "438699 3 146233", "146233 257 569", "569 569 1" ]

4615006

2 11 89 2357

[ "4615006 2 2307503", "2307503 11 209773", "209773 89 2357", "2357 2357 1" ]

2989950

2 3 5 5 31 643

[ "2989950 2 1494975", "1494975 3 498325", "498325 5 99665", "99665 5 19933", "19933 31 643", "643 643 1" ]

949144

2 2 2 7 17 997

[ "949144 2 474572", "474572 2 237286", "237286 2 118643", "118643 7 16949", "16949 17 997", "997 997 1" ]

2960159

17 31 41 137

[ "2960159 17 174127", "174127 31 5617", "5617 41 137", "137 137 1" ]

962525

5 5 38501

[ "962525 5 192505", "192505 5 38501", "38501 38501 1" ]

601762

2 7 53 811

[ "601762 2 300881", "300881 7 42983", "42983 53 811", "811 811 1" ]

3636983

7 43 43 281

[ "3636983 7 519569", "519569 43 12083", "12083 43 281", "281 281 1" ]

4674788

2 2 43 27179

[ "4674788 2 2337394", "2337394 2 1168697", "1168697 43 27179", "27179 27179 1" ]

2564868

2 2 3 23 9293

[ "2564868 2 1282434", "1282434 2 641217", "641217 3 213739", "213739 23 9293", "9293 9293 1" ]

4978088

2 2 2 61 101 101

[ "4978088 2 2489044", "2489044 2 1244522", "1244522 2 622261", "622261 61 10201", "10201 101 101", "101 101 1" ]

4019268

2 2 3 11 30449

[ "4019268 2 2009634", "2009634 2 1004817", "1004817 3 334939", "334939 11 30449", "30449 30449 1" ]

3879698

2 173 11213

[ "3879698 2 1939849", "1939849 173 11213", "11213 11213 1" ]

4960375

5 5 5 7 5669

[ "4960375 5 992075", "992075 5 198415", "198415 5 39683", "39683 7 5669", "5669 5669 1" ]

3006308

2 2 47 15991

[ "3006308 2 1503154", "1503154 2 751577", "751577 47 15991", "15991 15991 1" ]

1614895

5 71 4549

[ "1614895 5 322979", "322979 71 4549", "4549 4549 1" ]

3537361

47 73 1031

[ "3537361 47 75263", "75263 73 1031", "1031 1031 1" ]

2350018

2 11 37 2887

[ "2350018 2 1175009", "1175009 11 106819", "106819 37 2887", "2887 2887 1" ]

4676255

5 41 22811

[ "4676255 5 935251", "935251 41 22811", "22811 22811 1" ]

3164917

7 452131

[ "3164917 7 452131", "452131 452131 1" ]

1866636

2 2 3 3 19 2729

[ "1866636 2 933318", "933318 2 466659", "466659 3 155553", "155553 3 51851", "51851 19 2729", "2729 2729 1" ]

1479304

2 2 2 184913

[ "1479304 2 739652", "739652 2 369826", "369826 2 184913", "184913 184913 1" ]

2070773

47 44059

[ "2070773 47 44059", "44059 44059 1" ]

3567743

89 40087

[ "3567743 89 40087", "40087 40087 1" ]