yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
3770308	2 2 942577	[ "3770308 2 1885154", "1885154 2 942577", "942577 942577 1" ]
1515350	2 5 5 30307	[ "1515350 2 757675", "757675 5 151535", "151535 5 30307", "30307 30307 1" ]
905500	2 2 5 5 5 1811	[ "905500 2 452750", "452750 2 226375", "226375 5 45275", "45275 5 9055", "9055 5 1811", "1811 1811 1" ]
1806101	11 164191	[ "1806101 11 164191", "164191 164191 1" ]
1625865	3 5 107 1013	[ "1625865 3 541955", "541955 5 108391", "108391 107 1013", "1013 1013 1" ]
1445891	107 13513	[ "1445891 107 13513", "13513 13513 1" ]
2963111	41 72271	[ "2963111 41 72271", "72271 72271 1" ]
679599	3 3 75511	[ "679599 3 226533", "226533 3 75511", "75511 75511 1" ]
3218958	2 3 3 178831	[ "3218958 2 1609479", "1609479 3 536493", "536493 3 178831", "178831 178831 1" ]
3700418	2 433 4273	[ "3700418 2 1850209", "1850209 433 4273", "4273 4273 1" ]
3184654	2 11 144757	[ "3184654 2 1592327", "1592327 11 144757", "144757 144757 1" ]
33292	2 2 7 29 41	[ "33292 2 16646", "16646 2 8323", "8323 7 1189", "1189 29 41", "41 41 1" ]
1071218	2 535609	[ "1071218 2 535609", "535609 535609 1" ]
3390929	61 55589	[ "3390929 61 55589", "55589 55589 1" ]
4809396	2 2 3 241 1663	[ "4809396 2 2404698", "2404698 2 1202349", "1202349 3 400783", "400783 241 1663", "1663 1663 1" ]
1089715	5 11 19813	[ "1089715 5 217943", "217943 11 19813", "19813 19813 1" ]
127241	127241	[ "127241 127241 1" ]
2172068	2 2 543017	[ "2172068 2 1086034", "1086034 2 543017", "543017 543017 1" ]
2894177	11 13 37 547	[ "2894177 11 263107", "263107 13 20239", "20239 37 547", "547 547 1" ]
317	317	[ "317 317 1" ]
2525060	2 2 5 251 503	[ "2525060 2 1262530", "1262530 2 631265", "631265 5 126253", "126253 251 503", "503 503 1" ]
2757685	5 7 78791	[ "2757685 5 551537", "551537 7 78791", "78791 78791 1" ]
1335456	2 2 2 2 2 3 3 4637	[ "1335456 2 667728", "667728 2 333864", "333864 2 166932", "166932 2 83466", "83466 2 41733", "41733 3 13911", "13911 3 4637", "4637 4637 1" ]
4089001	7 7 83449	[ "4089001 7 584143", "584143 7 83449", "83449 83449 1" ]
4292206	2 2146103	[ "4292206 2 2146103", "2146103 2146103 1" ]
3958175	5 5 13 19 641	[ "3958175 5 791635", "791635 5 158327", "158327 13 12179", "12179 19 641", "641 641 1" ]
2425502	2 19 29 31 71	[ "2425502 2 1212751", "1212751 19 63829", "63829 29 2201", "2201 31 71", "71 71 1" ]
4078099	4078099	[ "4078099 4078099 1" ]
481265	5 101 953	[ "481265 5 96253", "96253 101 953", "953 953 1" ]
2994886	2 41 36523	[ "2994886 2 1497443", "1497443 41 36523", "36523 36523 1" ]
1057392	2 2 2 2 3 3 7 1049	[ "1057392 2 528696", "528696 2 264348", "264348 2 132174", "132174 2 66087", "66087 3 22029", "22029 3 7343", "7343 7 1049", "1049 1049 1" ]
2547627	3 73 11633	[ "2547627 3 849209", "849209 73 11633", "11633 11633 1" ]
204901	17 17 709	[ "204901 17 12053", "12053 17 709", "709 709 1" ]
2046612	2 2 3 170551	[ "2046612 2 1023306", "1023306 2 511653", "511653 3 170551", "170551 170551 1" ]
973128	2 2 2 3 13 3119	[ "973128 2 486564", "486564 2 243282", "243282 2 121641", "121641 3 40547", "40547 13 3119", "3119 3119 1" ]
2636417	7 376631	[ "2636417 7 376631", "376631 376631 1" ]
1952148	2 2 3 11 23 643	[ "1952148 2 976074", "976074 2 488037", "488037 3 162679", "162679 11 14789", "14789 23 643", "643 643 1" ]
2219507	31 71597	[ "2219507 31 71597", "71597 71597 1" ]
3368961	3 3 37 67 151	[ "3368961 3 1122987", "1122987 3 374329", "374329 37 10117", "10117 67 151", "151 151 1" ]
1074830	2 5 19 5657	[ "1074830 2 537415", "537415 5 107483", "107483 19 5657", "5657 5657 1" ]
4297809	3 31 37 1249	[ "4297809 3 1432603", "1432603 31 46213", "46213 37 1249", "1249 1249 1" ]
262275	3 5 5 13 269	[ "262275 3 87425", "87425 5 17485", "17485 5 3497", "3497 13 269", "269 269 1" ]
1484791	7 11 11 1753	[ "1484791 7 212113", "212113 11 19283", "19283 11 1753", "1753 1753 1" ]
2814150	2 3 5 5 73 257	[ "2814150 2 1407075", "1407075 3 469025", "469025 5 93805", "93805 5 18761", "18761 73 257", "257 257 1" ]
2131553	19 43 2609	[ "2131553 19 112187", "112187 43 2609", "2609 2609 1" ]
1994866	2 997433	[ "1994866 2 997433", "997433 997433 1" ]
321724	2 2 13 23 269	[ "321724 2 160862", "160862 2 80431", "80431 13 6187", "6187 23 269", "269 269 1" ]
3894130	2 5 23 16931	[ "3894130 2 1947065", "1947065 5 389413", "389413 23 16931", "16931 16931 1" ]
565328	2 2 2 2 89 397	[ "565328 2 282664", "282664 2 141332", "141332 2 70666", "70666 2 35333", "35333 89 397", "397 397 1" ]
2199278	2 43 107 239	[ "2199278 2 1099639", "1099639 43 25573", "25573 107 239", "239 239 1" ]
3798122	2 1291 1471	[ "3798122 2 1899061", "1899061 1291 1471", "1471 1471 1" ]
2686217	2686217	[ "2686217 2686217 1" ]
1689361	569 2969	[ "1689361 569 2969", "2969 2969 1" ]
3047289	3 7 145109	[ "3047289 3 1015763", "1015763 7 145109", "145109 145109 1" ]
4436190	2 3 3 5 11 4481	[ "4436190 2 2218095", "2218095 3 739365", "739365 3 246455", "246455 5 49291", "49291 11 4481", "4481 4481 1" ]
1570773	3 293 1787	[ "1570773 3 523591", "523591 293 1787", "1787 1787 1" ]
2413400	2 2 2 5 5 11 1097	[ "2413400 2 1206700", "1206700 2 603350", "603350 2 301675", "301675 5 60335", "60335 5 12067", "12067 11 1097", "1097 1097 1" ]
3018915	3 3 5 73 919	[ "3018915 3 1006305", "1006305 3 335435", "335435 5 67087", "67087 73 919", "919 919 1" ]
4219211	4219211	[ "4219211 4219211 1" ]
1758048	2 2 2 2 2 3 18313	[ "1758048 2 879024", "879024 2 439512", "439512 2 219756", "219756 2 109878", "109878 2 54939", "54939 3 18313", "18313 18313 1" ]
3016756	2 2 349 2161	[ "3016756 2 1508378", "1508378 2 754189", "754189 349 2161", "2161 2161 1" ]
3061237	3061237	[ "3061237 3061237 1" ]
590264	2 2 2 73783	[ "590264 2 295132", "295132 2 147566", "147566 2 73783", "73783 73783 1" ]
2402605	5 480521	[ "2402605 5 480521", "480521 480521 1" ]
661559	673 983	[ "661559 673 983", "983 983 1" ]
3570408	2 2 2 3 3 17 2917	[ "3570408 2 1785204", "1785204 2 892602", "892602 2 446301", "446301 3 148767", "148767 3 49589", "49589 17 2917", "2917 2917 1" ]
2730958	2 137 9967	[ "2730958 2 1365479", "1365479 137 9967", "9967 9967 1" ]
1403495	5 280699	[ "1403495 5 280699", "280699 280699 1" ]
504272	2 2 2 2 31517	[ "504272 2 252136", "252136 2 126068", "126068 2 63034", "63034 2 31517", "31517 31517 1" ]
2887327	29 99563	[ "2887327 29 99563", "99563 99563 1" ]
3728150	2 5 5 173 431	[ "3728150 2 1864075", "1864075 5 372815", "372815 5 74563", "74563 173 431", "431 431 1" ]
3270399	3 11 99103	[ "3270399 3 1090133", "1090133 11 99103", "99103 99103 1" ]
1084673	1084673	[ "1084673 1084673 1" ]
2087011	2087011	[ "2087011 2087011 1" ]
633463	633463	[ "633463 633463 1" ]
912329	11 82939	[ "912329 11 82939", "82939 82939 1" ]
2790532	2 2 293 2381	[ "2790532 2 1395266", "1395266 2 697633", "697633 293 2381", "2381 2381 1" ]
4949823	3 19 37 2347	[ "4949823 3 1649941", "1649941 19 86839", "86839 37 2347", "2347 2347 1" ]
2691418	2 281 4789	[ "2691418 2 1345709", "1345709 281 4789", "4789 4789 1" ]
2585001	3 149 5783	[ "2585001 3 861667", "861667 149 5783", "5783 5783 1" ]
3628631	3628631	[ "3628631 3628631 1" ]
2547536	2 2 2 2 89 1789	[ "2547536 2 1273768", "1273768 2 636884", "636884 2 318442", "318442 2 159221", "159221 89 1789", "1789 1789 1" ]
990134	2 495067	[ "990134 2 495067", "495067 495067 1" ]
1925127	3 3 3 3 23767	[ "1925127 3 641709", "641709 3 213903", "213903 3 71301", "71301 3 23767", "23767 23767 1" ]
3310317	3 3 103 3571	[ "3310317 3 1103439", "1103439 3 367813", "367813 103 3571", "3571 3571 1" ]
3164493	3 1054831	[ "3164493 3 1054831", "1054831 1054831 1" ]
3000080	2 2 2 2 5 37501	[ "3000080 2 1500040", "1500040 2 750020", "750020 2 375010", "375010 2 187505", "187505 5 37501", "37501 37501 1" ]
1665669	3 107 5189	[ "1665669 3 555223", "555223 107 5189", "5189 5189 1" ]
4110089	4110089	[ "4110089 4110089 1" ]
3133337	3133337	[ "3133337 3133337 1" ]
3640496	2 2 2 2 227531	[ "3640496 2 1820248", "1820248 2 910124", "910124 2 455062", "455062 2 227531", "227531 227531 1" ]
3854373	3 1284791	[ "3854373 3 1284791", "1284791 1284791 1" ]
225101	23 9787	[ "225101 23 9787", "9787 9787 1" ]
503486	2 227 1109	[ "503486 2 251743", "251743 227 1109", "1109 1109 1" ]
1308032	2 2 2 2 2 2 2 11 929	[ "1308032 2 654016", "654016 2 327008", "327008 2 163504", "163504 2 81752", "81752 2 40876", "40876 2 20438", "20438 2 10219", "10219 11 929", "929 929 1" ]
2988665	5 463 1291	[ "2988665 5 597733", "597733 463 1291", "1291 1291 1" ]
2886721	307 9403	[ "2886721 307 9403", "9403 9403 1" ]
382698	2 3 3 3 19 373	[ "382698 2 191349", "191349 3 63783", "63783 3 21261", "21261 3 7087", "7087 19 373", "373 373 1" ]
1778771	109 16319	[ "1778771 109 16319", "16319 16319 1" ]
3713324	2 2 928331	[ "3713324 2 1856662", "1856662 2 928331", "928331 928331 1" ]

3770308

2 2 942577

[ "3770308 2 1885154", "1885154 2 942577", "942577 942577 1" ]

1515350

2 5 5 30307

[ "1515350 2 757675", "757675 5 151535", "151535 5 30307", "30307 30307 1" ]

905500

2 2 5 5 5 1811

[ "905500 2 452750", "452750 2 226375", "226375 5 45275", "45275 5 9055", "9055 5 1811", "1811 1811 1" ]

1806101

11 164191

[ "1806101 11 164191", "164191 164191 1" ]

1625865

3 5 107 1013

[ "1625865 3 541955", "541955 5 108391", "108391 107 1013", "1013 1013 1" ]

1445891

107 13513

[ "1445891 107 13513", "13513 13513 1" ]

2963111

41 72271

[ "2963111 41 72271", "72271 72271 1" ]

679599

3 3 75511

[ "679599 3 226533", "226533 3 75511", "75511 75511 1" ]

3218958

2 3 3 178831

[ "3218958 2 1609479", "1609479 3 536493", "536493 3 178831", "178831 178831 1" ]

3700418

2 433 4273

[ "3700418 2 1850209", "1850209 433 4273", "4273 4273 1" ]

3184654

2 11 144757

[ "3184654 2 1592327", "1592327 11 144757", "144757 144757 1" ]

33292

2 2 7 29 41

[ "33292 2 16646", "16646 2 8323", "8323 7 1189", "1189 29 41", "41 41 1" ]

1071218

2 535609

[ "1071218 2 535609", "535609 535609 1" ]

3390929

61 55589

[ "3390929 61 55589", "55589 55589 1" ]

4809396

2 2 3 241 1663

[ "4809396 2 2404698", "2404698 2 1202349", "1202349 3 400783", "400783 241 1663", "1663 1663 1" ]

1089715

5 11 19813

[ "1089715 5 217943", "217943 11 19813", "19813 19813 1" ]

127241

[ "127241 127241 1" ]

2172068

2 2 543017

[ "2172068 2 1086034", "1086034 2 543017", "543017 543017 1" ]

2894177

11 13 37 547

[ "2894177 11 263107", "263107 13 20239", "20239 37 547", "547 547 1" ]

317

[ "317 317 1" ]

2525060

2 2 5 251 503

[ "2525060 2 1262530", "1262530 2 631265", "631265 5 126253", "126253 251 503", "503 503 1" ]

2757685

5 7 78791

[ "2757685 5 551537", "551537 7 78791", "78791 78791 1" ]

1335456

2 2 2 2 2 3 3 4637

[ "1335456 2 667728", "667728 2 333864", "333864 2 166932", "166932 2 83466", "83466 2 41733", "41733 3 13911", "13911 3 4637", "4637 4637 1" ]

4089001

7 7 83449

[ "4089001 7 584143", "584143 7 83449", "83449 83449 1" ]

4292206

2 2146103

[ "4292206 2 2146103", "2146103 2146103 1" ]

3958175

5 5 13 19 641

[ "3958175 5 791635", "791635 5 158327", "158327 13 12179", "12179 19 641", "641 641 1" ]

2425502

2 19 29 31 71

[ "2425502 2 1212751", "1212751 19 63829", "63829 29 2201", "2201 31 71", "71 71 1" ]

4078099

[ "4078099 4078099 1" ]

481265

5 101 953

[ "481265 5 96253", "96253 101 953", "953 953 1" ]

2994886

2 41 36523

[ "2994886 2 1497443", "1497443 41 36523", "36523 36523 1" ]

1057392

2 2 2 2 3 3 7 1049

[ "1057392 2 528696", "528696 2 264348", "264348 2 132174", "132174 2 66087", "66087 3 22029", "22029 3 7343", "7343 7 1049", "1049 1049 1" ]

2547627

3 73 11633

[ "2547627 3 849209", "849209 73 11633", "11633 11633 1" ]

204901

17 17 709

[ "204901 17 12053", "12053 17 709", "709 709 1" ]

2046612

2 2 3 170551

[ "2046612 2 1023306", "1023306 2 511653", "511653 3 170551", "170551 170551 1" ]

973128

2 2 2 3 13 3119

[ "973128 2 486564", "486564 2 243282", "243282 2 121641", "121641 3 40547", "40547 13 3119", "3119 3119 1" ]

2636417

7 376631

[ "2636417 7 376631", "376631 376631 1" ]

1952148

2 2 3 11 23 643

[ "1952148 2 976074", "976074 2 488037", "488037 3 162679", "162679 11 14789", "14789 23 643", "643 643 1" ]

2219507

31 71597

[ "2219507 31 71597", "71597 71597 1" ]

3368961

3 3 37 67 151

[ "3368961 3 1122987", "1122987 3 374329", "374329 37 10117", "10117 67 151", "151 151 1" ]

1074830

2 5 19 5657

[ "1074830 2 537415", "537415 5 107483", "107483 19 5657", "5657 5657 1" ]

4297809

3 31 37 1249

[ "4297809 3 1432603", "1432603 31 46213", "46213 37 1249", "1249 1249 1" ]

262275

3 5 5 13 269

[ "262275 3 87425", "87425 5 17485", "17485 5 3497", "3497 13 269", "269 269 1" ]

1484791

7 11 11 1753

[ "1484791 7 212113", "212113 11 19283", "19283 11 1753", "1753 1753 1" ]

2814150

2 3 5 5 73 257

[ "2814150 2 1407075", "1407075 3 469025", "469025 5 93805", "93805 5 18761", "18761 73 257", "257 257 1" ]

2131553

19 43 2609

[ "2131553 19 112187", "112187 43 2609", "2609 2609 1" ]

1994866

2 997433

[ "1994866 2 997433", "997433 997433 1" ]

321724

2 2 13 23 269

[ "321724 2 160862", "160862 2 80431", "80431 13 6187", "6187 23 269", "269 269 1" ]

3894130

2 5 23 16931

[ "3894130 2 1947065", "1947065 5 389413", "389413 23 16931", "16931 16931 1" ]

565328

2 2 2 2 89 397

[ "565328 2 282664", "282664 2 141332", "141332 2 70666", "70666 2 35333", "35333 89 397", "397 397 1" ]

2199278

2 43 107 239

[ "2199278 2 1099639", "1099639 43 25573", "25573 107 239", "239 239 1" ]

3798122

2 1291 1471

[ "3798122 2 1899061", "1899061 1291 1471", "1471 1471 1" ]

2686217

[ "2686217 2686217 1" ]

1689361

569 2969

[ "1689361 569 2969", "2969 2969 1" ]

3047289

3 7 145109

[ "3047289 3 1015763", "1015763 7 145109", "145109 145109 1" ]

4436190

2 3 3 5 11 4481

[ "4436190 2 2218095", "2218095 3 739365", "739365 3 246455", "246455 5 49291", "49291 11 4481", "4481 4481 1" ]

1570773

3 293 1787

[ "1570773 3 523591", "523591 293 1787", "1787 1787 1" ]

2413400

2 2 2 5 5 11 1097

[ "2413400 2 1206700", "1206700 2 603350", "603350 2 301675", "301675 5 60335", "60335 5 12067", "12067 11 1097", "1097 1097 1" ]

3018915

3 3 5 73 919

[ "3018915 3 1006305", "1006305 3 335435", "335435 5 67087", "67087 73 919", "919 919 1" ]

4219211

[ "4219211 4219211 1" ]

1758048

2 2 2 2 2 3 18313

[ "1758048 2 879024", "879024 2 439512", "439512 2 219756", "219756 2 109878", "109878 2 54939", "54939 3 18313", "18313 18313 1" ]

3016756

2 2 349 2161

[ "3016756 2 1508378", "1508378 2 754189", "754189 349 2161", "2161 2161 1" ]

3061237

[ "3061237 3061237 1" ]

590264

2 2 2 73783

[ "590264 2 295132", "295132 2 147566", "147566 2 73783", "73783 73783 1" ]

2402605

5 480521

[ "2402605 5 480521", "480521 480521 1" ]

661559

673 983

[ "661559 673 983", "983 983 1" ]

3570408

2 2 2 3 3 17 2917

[ "3570408 2 1785204", "1785204 2 892602", "892602 2 446301", "446301 3 148767", "148767 3 49589", "49589 17 2917", "2917 2917 1" ]

2730958

2 137 9967

[ "2730958 2 1365479", "1365479 137 9967", "9967 9967 1" ]

1403495

5 280699

[ "1403495 5 280699", "280699 280699 1" ]

504272

2 2 2 2 31517

[ "504272 2 252136", "252136 2 126068", "126068 2 63034", "63034 2 31517", "31517 31517 1" ]

2887327

29 99563

[ "2887327 29 99563", "99563 99563 1" ]

3728150

2 5 5 173 431

[ "3728150 2 1864075", "1864075 5 372815", "372815 5 74563", "74563 173 431", "431 431 1" ]

3270399

3 11 99103

[ "3270399 3 1090133", "1090133 11 99103", "99103 99103 1" ]

1084673

[ "1084673 1084673 1" ]

2087011

[ "2087011 2087011 1" ]

633463

[ "633463 633463 1" ]

912329

11 82939

[ "912329 11 82939", "82939 82939 1" ]

2790532

2 2 293 2381

[ "2790532 2 1395266", "1395266 2 697633", "697633 293 2381", "2381 2381 1" ]

4949823

3 19 37 2347

[ "4949823 3 1649941", "1649941 19 86839", "86839 37 2347", "2347 2347 1" ]

2691418

2 281 4789

[ "2691418 2 1345709", "1345709 281 4789", "4789 4789 1" ]

2585001

3 149 5783

[ "2585001 3 861667", "861667 149 5783", "5783 5783 1" ]

3628631

[ "3628631 3628631 1" ]

2547536

2 2 2 2 89 1789

[ "2547536 2 1273768", "1273768 2 636884", "636884 2 318442", "318442 2 159221", "159221 89 1789", "1789 1789 1" ]

990134

2 495067

[ "990134 2 495067", "495067 495067 1" ]

1925127

3 3 3 3 23767

[ "1925127 3 641709", "641709 3 213903", "213903 3 71301", "71301 3 23767", "23767 23767 1" ]

3310317

3 3 103 3571

[ "3310317 3 1103439", "1103439 3 367813", "367813 103 3571", "3571 3571 1" ]

3164493

3 1054831

[ "3164493 3 1054831", "1054831 1054831 1" ]

3000080

2 2 2 2 5 37501

[ "3000080 2 1500040", "1500040 2 750020", "750020 2 375010", "375010 2 187505", "187505 5 37501", "37501 37501 1" ]

1665669

3 107 5189

[ "1665669 3 555223", "555223 107 5189", "5189 5189 1" ]

4110089

[ "4110089 4110089 1" ]

3133337

[ "3133337 3133337 1" ]

3640496

2 2 2 2 227531

[ "3640496 2 1820248", "1820248 2 910124", "910124 2 455062", "455062 2 227531", "227531 227531 1" ]

3854373

3 1284791

[ "3854373 3 1284791", "1284791 1284791 1" ]

225101

23 9787

[ "225101 23 9787", "9787 9787 1" ]

503486

2 227 1109

[ "503486 2 251743", "251743 227 1109", "1109 1109 1" ]

1308032

2 2 2 2 2 2 2 11 929

[ "1308032 2 654016", "654016 2 327008", "327008 2 163504", "163504 2 81752", "81752 2 40876", "40876 2 20438", "20438 2 10219", "10219 11 929", "929 929 1" ]

2988665

5 463 1291

[ "2988665 5 597733", "597733 463 1291", "1291 1291 1" ]

2886721

307 9403

[ "2886721 307 9403", "9403 9403 1" ]

382698

2 3 3 3 19 373

[ "382698 2 191349", "191349 3 63783", "63783 3 21261", "21261 3 7087", "7087 19 373", "373 373 1" ]

1778771

109 16319

[ "1778771 109 16319", "16319 16319 1" ]

3713324

2 2 928331

[ "3713324 2 1856662", "1856662 2 928331", "928331 928331 1" ]