yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1677686	2 73 11491	[ "1677686 2 838843", "838843 73 11491", "11491 11491 1" ]
1328806	2 664403	[ "1328806 2 664403", "664403 664403 1" ]
3245953	1009 3217	[ "3245953 1009 3217", "3217 3217 1" ]
3798098	2 1899049	[ "3798098 2 1899049", "1899049 1899049 1" ]
3877152	2 2 2 2 2 3 40387	[ "3877152 2 1938576", "1938576 2 969288", "969288 2 484644", "484644 2 242322", "242322 2 121161", "121161 3 40387", "40387 40387 1" ]
4373477	19 383 601	[ "4373477 19 230183", "230183 383 601", "601 601 1" ]
2597247	3 3 288583	[ "2597247 3 865749", "865749 3 288583", "288583 288583 1" ]
4436928	2 2 2 2 2 2 3 3 7703	[ "4436928 2 2218464", "2218464 2 1109232", "1109232 2 554616", "554616 2 277308", "277308 2 138654", "138654 2 69327", "69327 3 23109", "23109 3 7703", "7703 7703 1" ]
4569487	13 313 1123	[ "4569487 13 351499", "351499 313 1123", "1123 1123 1" ]
2422186	2 13 59 1579	[ "2422186 2 1211093", "1211093 13 93161", "93161 59 1579", "1579 1579 1" ]
714626	2 11 11 2953	[ "714626 2 357313", "357313 11 32483", "32483 11 2953", "2953 2953 1" ]
2511478	2 17 73867	[ "2511478 2 1255739", "1255739 17 73867", "73867 73867 1" ]
1597240	2 2 2 5 73 547	[ "1597240 2 798620", "798620 2 399310", "399310 2 199655", "199655 5 39931", "39931 73 547", "547 547 1" ]
3515771	7 421 1193	[ "3515771 7 502253", "502253 421 1193", "1193 1193 1" ]
3455042	2 1727521	[ "3455042 2 1727521", "1727521 1727521 1" ]
4187663	4187663	[ "4187663 4187663 1" ]
1939416	2 2 2 3 80809	[ "1939416 2 969708", "969708 2 484854", "484854 2 242427", "242427 3 80809", "80809 80809 1" ]
2409536	2 2 2 2 2 2 37649	[ "2409536 2 1204768", "1204768 2 602384", "602384 2 301192", "301192 2 150596", "150596 2 75298", "75298 2 37649", "37649 37649 1" ]
2349083	11 213553	[ "2349083 11 213553", "213553 213553 1" ]
2264580	2 2 3 3 5 23 547	[ "2264580 2 1132290", "1132290 2 566145", "566145 3 188715", "188715 3 62905", "62905 5 12581", "12581 23 547", "547 547 1" ]
3014298	2 3 3 7 47 509	[ "3014298 2 1507149", "1507149 3 502383", "502383 3 167461", "167461 7 23923", "23923 47 509", "509 509 1" ]
3934100	2 2 5 5 39341	[ "3934100 2 1967050", "1967050 2 983525", "983525 5 196705", "196705 5 39341", "39341 39341 1" ]
3526686	2 3 3 3 65309	[ "3526686 2 1763343", "1763343 3 587781", "587781 3 195927", "195927 3 65309", "65309 65309 1" ]
1484089	179 8291	[ "1484089 179 8291", "8291 8291 1" ]
3834277	61 239 263	[ "3834277 61 62857", "62857 239 263", "263 263 1" ]
1793435	5 7 51241	[ "1793435 5 358687", "358687 7 51241", "51241 51241 1" ]
4746007	7 31 21871	[ "4746007 7 678001", "678001 31 21871", "21871 21871 1" ]
2270244	2 2 3 189187	[ "2270244 2 1135122", "1135122 2 567561", "567561 3 189187", "189187 189187 1" ]
3497011	7 113 4421	[ "3497011 7 499573", "499573 113 4421", "4421 4421 1" ]
1061652	2 2 3 88471	[ "1061652 2 530826", "530826 2 265413", "265413 3 88471", "88471 88471 1" ]
2577024	2 2 2 2 2 2 2 3 3 2237	[ "2577024 2 1288512", "1288512 2 644256", "644256 2 322128", "322128 2 161064", "161064 2 80532", "80532 2 40266", "40266 2 20133", "20133 3 6711", "6711 3 2237", "2237 2237 1" ]
2610513	3 3 290057	[ "2610513 3 870171", "870171 3 290057", "290057 290057 1" ]
2734653	3 73 12487	[ "2734653 3 911551", "911551 73 12487", "12487 12487 1" ]
2948475	3 5 5 39313	[ "2948475 3 982825", "982825 5 196565", "196565 5 39313", "39313 39313 1" ]
292802	2 281 521	[ "292802 2 146401", "146401 281 521", "521 521 1" ]
979002	2 3 3 137 397	[ "979002 2 489501", "489501 3 163167", "163167 3 54389", "54389 137 397", "397 397 1" ]
1543620	2 2 3 5 13 1979	[ "1543620 2 771810", "771810 2 385905", "385905 3 128635", "128635 5 25727", "25727 13 1979", "1979 1979 1" ]
1021535	5 19 10753	[ "1021535 5 204307", "204307 19 10753", "10753 10753 1" ]
2435811	3 7 17 6823	[ "2435811 3 811937", "811937 7 115991", "115991 17 6823", "6823 6823 1" ]
4248037	4248037	[ "4248037 4248037 1" ]
2948842	2 13 113417	[ "2948842 2 1474421", "1474421 13 113417", "113417 113417 1" ]
2774277	3 3 3 11 9341	[ "2774277 3 924759", "924759 3 308253", "308253 3 102751", "102751 11 9341", "9341 9341 1" ]
4166753	293 14221	[ "4166753 293 14221", "14221 14221 1" ]
1035943	23 73 617	[ "1035943 23 45041", "45041 73 617", "617 617 1" ]
4754483	41 115963	[ "4754483 41 115963", "115963 115963 1" ]
1288607	1288607	[ "1288607 1288607 1" ]
4324685	5 19 45523	[ "4324685 5 864937", "864937 19 45523", "45523 45523 1" ]
1739451	3 7 7 11833	[ "1739451 3 579817", "579817 7 82831", "82831 7 11833", "11833 11833 1" ]
1324966	2 662483	[ "1324966 2 662483", "662483 662483 1" ]
2024507	19 127 839	[ "2024507 19 106553", "106553 127 839", "839 839 1" ]
576100	2 2 5 5 7 823	[ "576100 2 288050", "288050 2 144025", "144025 5 28805", "28805 5 5761", "5761 7 823", "823 823 1" ]
1186658	2 11 53939	[ "1186658 2 593329", "593329 11 53939", "53939 53939 1" ]
1387595	5 11 25229	[ "1387595 5 277519", "277519 11 25229", "25229 25229 1" ]
900746	2 7 11 5849	[ "900746 2 450373", "450373 7 64339", "64339 11 5849", "5849 5849 1" ]
3733888	2 2 2 2 2 2 2 31 941	[ "3733888 2 1866944", "1866944 2 933472", "933472 2 466736", "466736 2 233368", "233368 2 116684", "116684 2 58342", "58342 2 29171", "29171 31 941", "941 941 1" ]
4689058	2 11 213139	[ "4689058 2 2344529", "2344529 11 213139", "213139 213139 1" ]
4178353	43 97171	[ "4178353 43 97171", "97171 97171 1" ]
101262	2 3 7 2411	[ "101262 2 50631", "50631 3 16877", "16877 7 2411", "2411 2411 1" ]
3761995	5 23 32713	[ "3761995 5 752399", "752399 23 32713", "32713 32713 1" ]
4034393	11 29 12647	[ "4034393 11 366763", "366763 29 12647", "12647 12647 1" ]
2150641	2150641	[ "2150641 2150641 1" ]
4849254	2 3 3 3 89 1009	[ "4849254 2 2424627", "2424627 3 808209", "808209 3 269403", "269403 3 89801", "89801 89 1009", "1009 1009 1" ]
3322177	31 31 3457	[ "3322177 31 107167", "107167 31 3457", "3457 3457 1" ]
4941012	2 2 3 411751	[ "4941012 2 2470506", "2470506 2 1235253", "1235253 3 411751", "411751 411751 1" ]
2738782	2 1369391	[ "2738782 2 1369391", "1369391 1369391 1" ]
3305189	31 106619	[ "3305189 31 106619", "106619 106619 1" ]
3240515	5 739 877	[ "3240515 5 648103", "648103 739 877", "877 877 1" ]
1085061	3 361687	[ "1085061 3 361687", "361687 361687 1" ]
3225925	5 5 129037	[ "3225925 5 645185", "645185 5 129037", "129037 129037 1" ]
3687170	2 5 368717	[ "3687170 2 1843585", "1843585 5 368717", "368717 368717 1" ]
1751231	1751231	[ "1751231 1751231 1" ]
372037	372037	[ "372037 372037 1" ]
3193284	2 2 3 281 947	[ "3193284 2 1596642", "1596642 2 798321", "798321 3 266107", "266107 281 947", "947 947 1" ]
4347184	2 2 2 2 23 11813	[ "4347184 2 2173592", "2173592 2 1086796", "1086796 2 543398", "543398 2 271699", "271699 23 11813", "11813 11813 1" ]
4886652	2 2 3 407221	[ "4886652 2 2443326", "2443326 2 1221663", "1221663 3 407221", "407221 407221 1" ]
402649	13 47 659	[ "402649 13 30973", "30973 47 659", "659 659 1" ]
760962	2 3 126827	[ "760962 2 380481", "380481 3 126827", "126827 126827 1" ]
48849	3 19 857	[ "48849 3 16283", "16283 19 857", "857 857 1" ]
952981	952981	[ "952981 952981 1" ]
804989	804989	[ "804989 804989 1" ]
2568308	2 2 642077	[ "2568308 2 1284154", "1284154 2 642077", "642077 642077 1" ]
1321811	19 73 953	[ "1321811 19 69569", "69569 73 953", "953 953 1" ]
724179	3 241393	[ "724179 3 241393", "241393 241393 1" ]
3486209	3486209	[ "3486209 3486209 1" ]
1932728	2 2 2 7 34513	[ "1932728 2 966364", "966364 2 483182", "483182 2 241591", "241591 7 34513", "34513 34513 1" ]
1348080	2 2 2 2 3 5 41 137	[ "1348080 2 674040", "674040 2 337020", "337020 2 168510", "168510 2 84255", "84255 3 28085", "28085 5 5617", "5617 41 137", "137 137 1" ]
4576315	5 17 17 3167	[ "4576315 5 915263", "915263 17 53839", "53839 17 3167", "3167 3167 1" ]
993043	37 26839	[ "993043 37 26839", "26839 26839 1" ]
998811	3 3 3 3 11 19 59	[ "998811 3 332937", "332937 3 110979", "110979 3 36993", "36993 3 12331", "12331 11 1121", "1121 19 59", "59 59 1" ]
3636208	2 2 2 2 23 41 241	[ "3636208 2 1818104", "1818104 2 909052", "909052 2 454526", "454526 2 227263", "227263 23 9881", "9881 41 241", "241 241 1" ]
1063854	2 3 3 3 3 3 11 199	[ "1063854 2 531927", "531927 3 177309", "177309 3 59103", "59103 3 19701", "19701 3 6567", "6567 3 2189", "2189 11 199", "199 199 1" ]
4749064	2 2 2 593633	[ "4749064 2 2374532", "2374532 2 1187266", "1187266 2 593633", "593633 593633 1" ]
1748423	43 73 557	[ "1748423 43 40661", "40661 73 557", "557 557 1" ]
3061525	5 5 151 811	[ "3061525 5 612305", "612305 5 122461", "122461 151 811", "811 811 1" ]
1119605	5 223921	[ "1119605 5 223921", "223921 223921 1" ]
4795110	2 3 3 5 53279	[ "4795110 2 2397555", "2397555 3 799185", "799185 3 266395", "266395 5 53279", "53279 53279 1" ]
2745932	2 2 7 281 349	[ "2745932 2 1372966", "1372966 2 686483", "686483 7 98069", "98069 281 349", "349 349 1" ]
441641	29 97 157	[ "441641 29 15229", "15229 97 157", "157 157 1" ]
252422	2 126211	[ "252422 2 126211", "126211 126211 1" ]
625736	2 2 2 17 43 107	[ "625736 2 312868", "312868 2 156434", "156434 2 78217", "78217 17 4601", "4601 43 107", "107 107 1" ]

1677686

2 73 11491

[ "1677686 2 838843", "838843 73 11491", "11491 11491 1" ]

1328806

2 664403

[ "1328806 2 664403", "664403 664403 1" ]

3245953

1009 3217

[ "3245953 1009 3217", "3217 3217 1" ]

3798098

2 1899049

[ "3798098 2 1899049", "1899049 1899049 1" ]

3877152

2 2 2 2 2 3 40387

[ "3877152 2 1938576", "1938576 2 969288", "969288 2 484644", "484644 2 242322", "242322 2 121161", "121161 3 40387", "40387 40387 1" ]

4373477

19 383 601

[ "4373477 19 230183", "230183 383 601", "601 601 1" ]

2597247

3 3 288583

[ "2597247 3 865749", "865749 3 288583", "288583 288583 1" ]

4436928

2 2 2 2 2 2 3 3 7703

[ "4436928 2 2218464", "2218464 2 1109232", "1109232 2 554616", "554616 2 277308", "277308 2 138654", "138654 2 69327", "69327 3 23109", "23109 3 7703", "7703 7703 1" ]

4569487

13 313 1123

[ "4569487 13 351499", "351499 313 1123", "1123 1123 1" ]

2422186

2 13 59 1579

[ "2422186 2 1211093", "1211093 13 93161", "93161 59 1579", "1579 1579 1" ]

714626

2 11 11 2953

[ "714626 2 357313", "357313 11 32483", "32483 11 2953", "2953 2953 1" ]

2511478

2 17 73867

[ "2511478 2 1255739", "1255739 17 73867", "73867 73867 1" ]

1597240

2 2 2 5 73 547

[ "1597240 2 798620", "798620 2 399310", "399310 2 199655", "199655 5 39931", "39931 73 547", "547 547 1" ]

3515771

7 421 1193

[ "3515771 7 502253", "502253 421 1193", "1193 1193 1" ]

3455042

2 1727521

[ "3455042 2 1727521", "1727521 1727521 1" ]

4187663

[ "4187663 4187663 1" ]

1939416

2 2 2 3 80809

[ "1939416 2 969708", "969708 2 484854", "484854 2 242427", "242427 3 80809", "80809 80809 1" ]

2409536

2 2 2 2 2 2 37649

[ "2409536 2 1204768", "1204768 2 602384", "602384 2 301192", "301192 2 150596", "150596 2 75298", "75298 2 37649", "37649 37649 1" ]

2349083

11 213553

[ "2349083 11 213553", "213553 213553 1" ]

2264580

2 2 3 3 5 23 547

[ "2264580 2 1132290", "1132290 2 566145", "566145 3 188715", "188715 3 62905", "62905 5 12581", "12581 23 547", "547 547 1" ]

3014298

2 3 3 7 47 509

[ "3014298 2 1507149", "1507149 3 502383", "502383 3 167461", "167461 7 23923", "23923 47 509", "509 509 1" ]

3934100

2 2 5 5 39341

[ "3934100 2 1967050", "1967050 2 983525", "983525 5 196705", "196705 5 39341", "39341 39341 1" ]

3526686

2 3 3 3 65309

[ "3526686 2 1763343", "1763343 3 587781", "587781 3 195927", "195927 3 65309", "65309 65309 1" ]

1484089

179 8291

[ "1484089 179 8291", "8291 8291 1" ]

3834277

61 239 263

[ "3834277 61 62857", "62857 239 263", "263 263 1" ]

1793435

5 7 51241

[ "1793435 5 358687", "358687 7 51241", "51241 51241 1" ]

4746007

7 31 21871

[ "4746007 7 678001", "678001 31 21871", "21871 21871 1" ]

2270244

2 2 3 189187

[ "2270244 2 1135122", "1135122 2 567561", "567561 3 189187", "189187 189187 1" ]

3497011

7 113 4421

[ "3497011 7 499573", "499573 113 4421", "4421 4421 1" ]

1061652

2 2 3 88471

[ "1061652 2 530826", "530826 2 265413", "265413 3 88471", "88471 88471 1" ]

2577024

2 2 2 2 2 2 2 3 3 2237

[ "2577024 2 1288512", "1288512 2 644256", "644256 2 322128", "322128 2 161064", "161064 2 80532", "80532 2 40266", "40266 2 20133", "20133 3 6711", "6711 3 2237", "2237 2237 1" ]

2610513

3 3 290057

[ "2610513 3 870171", "870171 3 290057", "290057 290057 1" ]

2734653

3 73 12487

[ "2734653 3 911551", "911551 73 12487", "12487 12487 1" ]

2948475

3 5 5 39313

[ "2948475 3 982825", "982825 5 196565", "196565 5 39313", "39313 39313 1" ]

292802

2 281 521

[ "292802 2 146401", "146401 281 521", "521 521 1" ]

979002

2 3 3 137 397

[ "979002 2 489501", "489501 3 163167", "163167 3 54389", "54389 137 397", "397 397 1" ]

1543620

2 2 3 5 13 1979

[ "1543620 2 771810", "771810 2 385905", "385905 3 128635", "128635 5 25727", "25727 13 1979", "1979 1979 1" ]

1021535

5 19 10753

[ "1021535 5 204307", "204307 19 10753", "10753 10753 1" ]

2435811

3 7 17 6823

[ "2435811 3 811937", "811937 7 115991", "115991 17 6823", "6823 6823 1" ]

4248037

[ "4248037 4248037 1" ]

2948842

2 13 113417

[ "2948842 2 1474421", "1474421 13 113417", "113417 113417 1" ]

2774277

3 3 3 11 9341

[ "2774277 3 924759", "924759 3 308253", "308253 3 102751", "102751 11 9341", "9341 9341 1" ]

4166753

293 14221

[ "4166753 293 14221", "14221 14221 1" ]

1035943

23 73 617

[ "1035943 23 45041", "45041 73 617", "617 617 1" ]

4754483

41 115963

[ "4754483 41 115963", "115963 115963 1" ]

1288607

[ "1288607 1288607 1" ]

4324685

5 19 45523

[ "4324685 5 864937", "864937 19 45523", "45523 45523 1" ]

1739451

3 7 7 11833

[ "1739451 3 579817", "579817 7 82831", "82831 7 11833", "11833 11833 1" ]

1324966

2 662483

[ "1324966 2 662483", "662483 662483 1" ]

2024507

19 127 839

[ "2024507 19 106553", "106553 127 839", "839 839 1" ]

576100

2 2 5 5 7 823

[ "576100 2 288050", "288050 2 144025", "144025 5 28805", "28805 5 5761", "5761 7 823", "823 823 1" ]

1186658

2 11 53939

[ "1186658 2 593329", "593329 11 53939", "53939 53939 1" ]

1387595

5 11 25229

[ "1387595 5 277519", "277519 11 25229", "25229 25229 1" ]

900746

2 7 11 5849

[ "900746 2 450373", "450373 7 64339", "64339 11 5849", "5849 5849 1" ]

3733888

2 2 2 2 2 2 2 31 941

[ "3733888 2 1866944", "1866944 2 933472", "933472 2 466736", "466736 2 233368", "233368 2 116684", "116684 2 58342", "58342 2 29171", "29171 31 941", "941 941 1" ]

4689058

2 11 213139

[ "4689058 2 2344529", "2344529 11 213139", "213139 213139 1" ]

4178353

43 97171

[ "4178353 43 97171", "97171 97171 1" ]

101262

2 3 7 2411

[ "101262 2 50631", "50631 3 16877", "16877 7 2411", "2411 2411 1" ]

3761995

5 23 32713

[ "3761995 5 752399", "752399 23 32713", "32713 32713 1" ]

4034393

11 29 12647

[ "4034393 11 366763", "366763 29 12647", "12647 12647 1" ]

2150641

[ "2150641 2150641 1" ]

4849254

2 3 3 3 89 1009

[ "4849254 2 2424627", "2424627 3 808209", "808209 3 269403", "269403 3 89801", "89801 89 1009", "1009 1009 1" ]

3322177

31 31 3457

[ "3322177 31 107167", "107167 31 3457", "3457 3457 1" ]

4941012

2 2 3 411751

[ "4941012 2 2470506", "2470506 2 1235253", "1235253 3 411751", "411751 411751 1" ]

2738782

2 1369391

[ "2738782 2 1369391", "1369391 1369391 1" ]

3305189

31 106619

[ "3305189 31 106619", "106619 106619 1" ]

3240515

5 739 877

[ "3240515 5 648103", "648103 739 877", "877 877 1" ]

1085061

3 361687

[ "1085061 3 361687", "361687 361687 1" ]

3225925

5 5 129037

[ "3225925 5 645185", "645185 5 129037", "129037 129037 1" ]

3687170

2 5 368717

[ "3687170 2 1843585", "1843585 5 368717", "368717 368717 1" ]

1751231

[ "1751231 1751231 1" ]

372037

[ "372037 372037 1" ]

3193284

2 2 3 281 947

[ "3193284 2 1596642", "1596642 2 798321", "798321 3 266107", "266107 281 947", "947 947 1" ]

4347184

2 2 2 2 23 11813

[ "4347184 2 2173592", "2173592 2 1086796", "1086796 2 543398", "543398 2 271699", "271699 23 11813", "11813 11813 1" ]

4886652

2 2 3 407221

[ "4886652 2 2443326", "2443326 2 1221663", "1221663 3 407221", "407221 407221 1" ]

402649

13 47 659

[ "402649 13 30973", "30973 47 659", "659 659 1" ]

760962

2 3 126827

[ "760962 2 380481", "380481 3 126827", "126827 126827 1" ]

48849

3 19 857

[ "48849 3 16283", "16283 19 857", "857 857 1" ]

952981

[ "952981 952981 1" ]

804989

[ "804989 804989 1" ]

2568308

2 2 642077

[ "2568308 2 1284154", "1284154 2 642077", "642077 642077 1" ]

1321811

19 73 953

[ "1321811 19 69569", "69569 73 953", "953 953 1" ]

724179

3 241393

[ "724179 3 241393", "241393 241393 1" ]

3486209

[ "3486209 3486209 1" ]

1932728

2 2 2 7 34513

[ "1932728 2 966364", "966364 2 483182", "483182 2 241591", "241591 7 34513", "34513 34513 1" ]

1348080

2 2 2 2 3 5 41 137

[ "1348080 2 674040", "674040 2 337020", "337020 2 168510", "168510 2 84255", "84255 3 28085", "28085 5 5617", "5617 41 137", "137 137 1" ]

4576315

5 17 17 3167

[ "4576315 5 915263", "915263 17 53839", "53839 17 3167", "3167 3167 1" ]

993043

37 26839

[ "993043 37 26839", "26839 26839 1" ]

998811

3 3 3 3 11 19 59

[ "998811 3 332937", "332937 3 110979", "110979 3 36993", "36993 3 12331", "12331 11 1121", "1121 19 59", "59 59 1" ]

3636208

2 2 2 2 23 41 241

[ "3636208 2 1818104", "1818104 2 909052", "909052 2 454526", "454526 2 227263", "227263 23 9881", "9881 41 241", "241 241 1" ]

1063854

2 3 3 3 3 3 11 199

[ "1063854 2 531927", "531927 3 177309", "177309 3 59103", "59103 3 19701", "19701 3 6567", "6567 3 2189", "2189 11 199", "199 199 1" ]

4749064

2 2 2 593633

[ "4749064 2 2374532", "2374532 2 1187266", "1187266 2 593633", "593633 593633 1" ]

1748423

43 73 557

[ "1748423 43 40661", "40661 73 557", "557 557 1" ]

3061525

5 5 151 811

[ "3061525 5 612305", "612305 5 122461", "122461 151 811", "811 811 1" ]

1119605

5 223921

[ "1119605 5 223921", "223921 223921 1" ]

4795110

2 3 3 5 53279

[ "4795110 2 2397555", "2397555 3 799185", "799185 3 266395", "266395 5 53279", "53279 53279 1" ]

2745932

2 2 7 281 349

[ "2745932 2 1372966", "1372966 2 686483", "686483 7 98069", "98069 281 349", "349 349 1" ]

441641

29 97 157

[ "441641 29 15229", "15229 97 157", "157 157 1" ]

252422

2 126211

[ "252422 2 126211", "126211 126211 1" ]

625736

2 2 2 17 43 107

[ "625736 2 312868", "312868 2 156434", "156434 2 78217", "78217 17 4601", "4601 43 107", "107 107 1" ]