yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1656074	2 7 29 4079	[ "1656074 2 828037", "828037 7 118291", "118291 29 4079", "4079 4079 1" ]
1717037	7 245291	[ "1717037 7 245291", "245291 245291 1" ]
1616771	13 124367	[ "1616771 13 124367", "124367 124367 1" ]
2003791	157 12763	[ "2003791 157 12763", "12763 12763 1" ]
3579358	2 61 29339	[ "3579358 2 1789679", "1789679 61 29339", "29339 29339 1" ]
3062567	17 47 3833	[ "3062567 17 180151", "180151 47 3833", "3833 3833 1" ]
2444030	2 5 244403	[ "2444030 2 1222015", "1222015 5 244403", "244403 244403 1" ]
2095029	3 3 17 13693	[ "2095029 3 698343", "698343 3 232781", "232781 17 13693", "13693 13693 1" ]
912030	2 3 5 7 43 101	[ "912030 2 456015", "456015 3 152005", "152005 5 30401", "30401 7 4343", "4343 43 101", "101 101 1" ]
4589000	2 2 2 5 5 5 13 353	[ "4589000 2 2294500", "2294500 2 1147250", "1147250 2 573625", "573625 5 114725", "114725 5 22945", "22945 5 4589", "4589 13 353", "353 353 1" ]
436489	37 47 251	[ "436489 37 11797", "11797 47 251", "251 251 1" ]
3250506	2 3 7 193 401	[ "3250506 2 1625253", "1625253 3 541751", "541751 7 77393", "77393 193 401", "401 401 1" ]
822683	822683	[ "822683 822683 1" ]
2104954	2 283 3719	[ "2104954 2 1052477", "1052477 283 3719", "3719 3719 1" ]
1299879	3 3 7 47 439	[ "1299879 3 433293", "433293 3 144431", "144431 7 20633", "20633 47 439", "439 439 1" ]
3654842	2 1827421	[ "3654842 2 1827421", "1827421 1827421 1" ]
2332217	83 28099	[ "2332217 83 28099", "28099 28099 1" ]
1616004	2 2 3 3 3 13 1151	[ "1616004 2 808002", "808002 2 404001", "404001 3 134667", "134667 3 44889", "44889 3 14963", "14963 13 1151", "1151 1151 1" ]
3953130	2 3 5 131771	[ "3953130 2 1976565", "1976565 3 658855", "658855 5 131771", "131771 131771 1" ]
2573245	5 514649	[ "2573245 5 514649", "514649 514649 1" ]
2169733	349 6217	[ "2169733 349 6217", "6217 6217 1" ]
2567722	2 353 3637	[ "2567722 2 1283861", "1283861 353 3637", "3637 3637 1" ]
4750524	2 2 3 3 131959	[ "4750524 2 2375262", "2375262 2 1187631", "1187631 3 395877", "395877 3 131959", "131959 131959 1" ]
387924	2 2 3 32327	[ "387924 2 193962", "193962 2 96981", "96981 3 32327", "32327 32327 1" ]
1497800	2 2 2 5 5 7489	[ "1497800 2 748900", "748900 2 374450", "374450 2 187225", "187225 5 37445", "37445 5 7489", "7489 7489 1" ]
3140287	373 8419	[ "3140287 373 8419", "8419 8419 1" ]
2134141	2134141	[ "2134141 2134141 1" ]
297537	3 41 41 59	[ "297537 3 99179", "99179 41 2419", "2419 41 59", "59 59 1" ]
1988367	3 662789	[ "1988367 3 662789", "662789 662789 1" ]
4614055	5 17 19 2857	[ "4614055 5 922811", "922811 17 54283", "54283 19 2857", "2857 2857 1" ]
506538	2 3 3 107 263	[ "506538 2 253269", "253269 3 84423", "84423 3 28141", "28141 107 263", "263 263 1" ]
1593130	2 5 7 11 2069	[ "1593130 2 796565", "796565 5 159313", "159313 7 22759", "22759 11 2069", "2069 2069 1" ]
3451733	127 27179	[ "3451733 127 27179", "27179 27179 1" ]
1401887	769 1823	[ "1401887 769 1823", "1823 1823 1" ]
4004860	2 2 5 17 11779	[ "4004860 2 2002430", "2002430 2 1001215", "1001215 5 200243", "200243 17 11779", "11779 11779 1" ]
1409880	2 2 2 3 5 31 379	[ "1409880 2 704940", "704940 2 352470", "352470 2 176235", "176235 3 58745", "58745 5 11749", "11749 31 379", "379 379 1" ]
321140	2 2 5 16057	[ "321140 2 160570", "160570 2 80285", "80285 5 16057", "16057 16057 1" ]
1957670	2 5 11 13 37 37	[ "1957670 2 978835", "978835 5 195767", "195767 11 17797", "17797 13 1369", "1369 37 37", "37 37 1" ]
813411	3 3 90379	[ "813411 3 271137", "271137 3 90379", "90379 90379 1" ]
4682181	3 7 59 3779	[ "4682181 3 1560727", "1560727 7 222961", "222961 59 3779", "3779 3779 1" ]
747808	2 2 2 2 2 23369	[ "747808 2 373904", "373904 2 186952", "186952 2 93476", "93476 2 46738", "46738 2 23369", "23369 23369 1" ]
1423144	2 2 2 177893	[ "1423144 2 711572", "711572 2 355786", "355786 2 177893", "177893 177893 1" ]
732788	2 2 7 26171	[ "732788 2 366394", "366394 2 183197", "183197 7 26171", "26171 26171 1" ]
1035309	3 11 137 229	[ "1035309 3 345103", "345103 11 31373", "31373 137 229", "229 229 1" ]
3680808	2 2 2 3 103 1489	[ "3680808 2 1840404", "1840404 2 920202", "920202 2 460101", "460101 3 153367", "153367 103 1489", "1489 1489 1" ]
3300009	3 71 15493	[ "3300009 3 1100003", "1100003 71 15493", "15493 15493 1" ]
2521244	2 2 11 57301	[ "2521244 2 1260622", "1260622 2 630311", "630311 11 57301", "57301 57301 1" ]
1948689	3 3 41 5281	[ "1948689 3 649563", "649563 3 216521", "216521 41 5281", "5281 5281 1" ]
929669	13 13 5501	[ "929669 13 71513", "71513 13 5501", "5501 5501 1" ]
805784	2 2 2 7 14389	[ "805784 2 402892", "402892 2 201446", "201446 2 100723", "100723 7 14389", "14389 14389 1" ]
4844455	5 7 11 12583	[ "4844455 5 968891", "968891 7 138413", "138413 11 12583", "12583 12583 1" ]
223630	2 5 11 19 107	[ "223630 2 111815", "111815 5 22363", "22363 11 2033", "2033 19 107", "107 107 1" ]
2123555	5 7 17 43 83	[ "2123555 5 424711", "424711 7 60673", "60673 17 3569", "3569 43 83", "83 83 1" ]
1244308	2 2 13 23929	[ "1244308 2 622154", "622154 2 311077", "311077 13 23929", "23929 23929 1" ]
3611027	7 515861	[ "3611027 7 515861", "515861 515861 1" ]
1308406	2 11 59473	[ "1308406 2 654203", "654203 11 59473", "59473 59473 1" ]
4231047	3 233 6053	[ "4231047 3 1410349", "1410349 233 6053", "6053 6053 1" ]
3982769	7 7 81281	[ "3982769 7 568967", "568967 7 81281", "81281 81281 1" ]
3753490	2 5 13 13 2221	[ "3753490 2 1876745", "1876745 5 375349", "375349 13 28873", "28873 13 2221", "2221 2221 1" ]
3257938	2 43 43 881	[ "3257938 2 1628969", "1628969 43 37883", "37883 43 881", "881 881 1" ]
3713876	2 2 928469	[ "3713876 2 1856938", "1856938 2 928469", "928469 928469 1" ]
3922891	7 7 7 11437	[ "3922891 7 560413", "560413 7 80059", "80059 7 11437", "11437 11437 1" ]
1148815	5 229763	[ "1148815 5 229763", "229763 229763 1" ]
535840	2 2 2 2 2 5 17 197	[ "535840 2 267920", "267920 2 133960", "133960 2 66980", "66980 2 33490", "33490 2 16745", "16745 5 3349", "3349 17 197", "197 197 1" ]
268085	5 53617	[ "268085 5 53617", "53617 53617 1" ]
1791269	1791269	[ "1791269 1791269 1" ]
1432521	3 3 159169	[ "1432521 3 477507", "477507 3 159169", "159169 159169 1" ]
363663	3 3 3 13469	[ "363663 3 121221", "121221 3 40407", "40407 3 13469", "13469 13469 1" ]
2278011	3 43 17659	[ "2278011 3 759337", "759337 43 17659", "17659 17659 1" ]
2403038	2 11 109229	[ "2403038 2 1201519", "1201519 11 109229", "109229 109229 1" ]
142606	2 113 631	[ "142606 2 71303", "71303 113 631", "631 631 1" ]
1136018	2 13 13 3361	[ "1136018 2 568009", "568009 13 43693", "43693 13 3361", "3361 3361 1" ]
4866946	2 7 41 61 139	[ "4866946 2 2433473", "2433473 7 347639", "347639 41 8479", "8479 61 139", "139 139 1" ]
127261	127261	[ "127261 127261 1" ]
748792	2 2 2 11 67 127	[ "748792 2 374396", "374396 2 187198", "187198 2 93599", "93599 11 8509", "8509 67 127", "127 127 1" ]
4970865	3 5 331391	[ "4970865 3 1656955", "1656955 5 331391", "331391 331391 1" ]
138173	7 19739	[ "138173 7 19739", "19739 19739 1" ]
1852396	2 2 7 7 13 727	[ "1852396 2 926198", "926198 2 463099", "463099 7 66157", "66157 7 9451", "9451 13 727", "727 727 1" ]
457489	79 5791	[ "457489 79 5791", "5791 5791 1" ]
1702763	47 36229	[ "1702763 47 36229", "36229 36229 1" ]
3190142	2 1595071	[ "3190142 2 1595071", "1595071 1595071 1" ]
671016	2 2 2 3 73 383	[ "671016 2 335508", "335508 2 167754", "167754 2 83877", "83877 3 27959", "27959 73 383", "383 383 1" ]
233863	7 33409	[ "233863 7 33409", "33409 33409 1" ]
4793866	2 7 7 11 4447	[ "4793866 2 2396933", "2396933 7 342419", "342419 7 48917", "48917 11 4447", "4447 4447 1" ]
4052926	2 2026463	[ "4052926 2 2026463", "2026463 2026463 1" ]
1436662	2 718331	[ "1436662 2 718331", "718331 718331 1" ]
1772162	2 7 126583	[ "1772162 2 886081", "886081 7 126583", "126583 126583 1" ]
1919737	31 61927	[ "1919737 31 61927", "61927 61927 1" ]
227917	59 3863	[ "227917 59 3863", "3863 3863 1" ]
4330311	3 1443437	[ "4330311 3 1443437", "1443437 1443437 1" ]
4090606	2 13 131 1201	[ "4090606 2 2045303", "2045303 13 157331", "157331 131 1201", "1201 1201 1" ]
4045045	5 823 983	[ "4045045 5 809009", "809009 823 983", "983 983 1" ]
3659915	5 7 53 1973	[ "3659915 5 731983", "731983 7 104569", "104569 53 1973", "1973 1973 1" ]
3252169	3252169	[ "3252169 3252169 1" ]
133403	133403	[ "133403 133403 1" ]
489094	2 244547	[ "489094 2 244547", "244547 244547 1" ]
90462	2 3 15077	[ "90462 2 45231", "45231 3 15077", "15077 15077 1" ]
1847047	19 97213	[ "1847047 19 97213", "97213 97213 1" ]
4619998	2 2309999	[ "4619998 2 2309999", "2309999 2309999 1" ]
4412005	5 13 103 659	[ "4412005 5 882401", "882401 13 67877", "67877 103 659", "659 659 1" ]

1656074

2 7 29 4079

[ "1656074 2 828037", "828037 7 118291", "118291 29 4079", "4079 4079 1" ]

1717037

7 245291

[ "1717037 7 245291", "245291 245291 1" ]

1616771

13 124367

[ "1616771 13 124367", "124367 124367 1" ]

2003791

157 12763

[ "2003791 157 12763", "12763 12763 1" ]

3579358

2 61 29339

[ "3579358 2 1789679", "1789679 61 29339", "29339 29339 1" ]

3062567

17 47 3833

[ "3062567 17 180151", "180151 47 3833", "3833 3833 1" ]

2444030

2 5 244403

[ "2444030 2 1222015", "1222015 5 244403", "244403 244403 1" ]

2095029

3 3 17 13693

[ "2095029 3 698343", "698343 3 232781", "232781 17 13693", "13693 13693 1" ]

912030

2 3 5 7 43 101

[ "912030 2 456015", "456015 3 152005", "152005 5 30401", "30401 7 4343", "4343 43 101", "101 101 1" ]

4589000

2 2 2 5 5 5 13 353

[ "4589000 2 2294500", "2294500 2 1147250", "1147250 2 573625", "573625 5 114725", "114725 5 22945", "22945 5 4589", "4589 13 353", "353 353 1" ]

436489

37 47 251

[ "436489 37 11797", "11797 47 251", "251 251 1" ]

3250506

2 3 7 193 401

[ "3250506 2 1625253", "1625253 3 541751", "541751 7 77393", "77393 193 401", "401 401 1" ]

822683

[ "822683 822683 1" ]

2104954

2 283 3719

[ "2104954 2 1052477", "1052477 283 3719", "3719 3719 1" ]

1299879

3 3 7 47 439

[ "1299879 3 433293", "433293 3 144431", "144431 7 20633", "20633 47 439", "439 439 1" ]

3654842

2 1827421

[ "3654842 2 1827421", "1827421 1827421 1" ]

2332217

83 28099

[ "2332217 83 28099", "28099 28099 1" ]

1616004

2 2 3 3 3 13 1151

[ "1616004 2 808002", "808002 2 404001", "404001 3 134667", "134667 3 44889", "44889 3 14963", "14963 13 1151", "1151 1151 1" ]

3953130

2 3 5 131771

[ "3953130 2 1976565", "1976565 3 658855", "658855 5 131771", "131771 131771 1" ]

2573245

5 514649

[ "2573245 5 514649", "514649 514649 1" ]

2169733

349 6217

[ "2169733 349 6217", "6217 6217 1" ]

2567722

2 353 3637

[ "2567722 2 1283861", "1283861 353 3637", "3637 3637 1" ]

4750524

2 2 3 3 131959

[ "4750524 2 2375262", "2375262 2 1187631", "1187631 3 395877", "395877 3 131959", "131959 131959 1" ]

387924

2 2 3 32327

[ "387924 2 193962", "193962 2 96981", "96981 3 32327", "32327 32327 1" ]

1497800

2 2 2 5 5 7489

[ "1497800 2 748900", "748900 2 374450", "374450 2 187225", "187225 5 37445", "37445 5 7489", "7489 7489 1" ]

3140287

373 8419

[ "3140287 373 8419", "8419 8419 1" ]

2134141

[ "2134141 2134141 1" ]

297537

3 41 41 59

[ "297537 3 99179", "99179 41 2419", "2419 41 59", "59 59 1" ]

1988367

3 662789

[ "1988367 3 662789", "662789 662789 1" ]

4614055

5 17 19 2857

[ "4614055 5 922811", "922811 17 54283", "54283 19 2857", "2857 2857 1" ]

506538

2 3 3 107 263

[ "506538 2 253269", "253269 3 84423", "84423 3 28141", "28141 107 263", "263 263 1" ]

1593130

2 5 7 11 2069

[ "1593130 2 796565", "796565 5 159313", "159313 7 22759", "22759 11 2069", "2069 2069 1" ]

3451733

127 27179

[ "3451733 127 27179", "27179 27179 1" ]

1401887

769 1823

[ "1401887 769 1823", "1823 1823 1" ]

4004860

2 2 5 17 11779

[ "4004860 2 2002430", "2002430 2 1001215", "1001215 5 200243", "200243 17 11779", "11779 11779 1" ]

1409880

2 2 2 3 5 31 379

[ "1409880 2 704940", "704940 2 352470", "352470 2 176235", "176235 3 58745", "58745 5 11749", "11749 31 379", "379 379 1" ]

321140

2 2 5 16057

[ "321140 2 160570", "160570 2 80285", "80285 5 16057", "16057 16057 1" ]

1957670

2 5 11 13 37 37

[ "1957670 2 978835", "978835 5 195767", "195767 11 17797", "17797 13 1369", "1369 37 37", "37 37 1" ]

813411

3 3 90379

[ "813411 3 271137", "271137 3 90379", "90379 90379 1" ]

4682181

3 7 59 3779

[ "4682181 3 1560727", "1560727 7 222961", "222961 59 3779", "3779 3779 1" ]

747808

2 2 2 2 2 23369

[ "747808 2 373904", "373904 2 186952", "186952 2 93476", "93476 2 46738", "46738 2 23369", "23369 23369 1" ]

1423144

2 2 2 177893

[ "1423144 2 711572", "711572 2 355786", "355786 2 177893", "177893 177893 1" ]

732788

2 2 7 26171

[ "732788 2 366394", "366394 2 183197", "183197 7 26171", "26171 26171 1" ]

1035309

3 11 137 229

[ "1035309 3 345103", "345103 11 31373", "31373 137 229", "229 229 1" ]

3680808

2 2 2 3 103 1489

[ "3680808 2 1840404", "1840404 2 920202", "920202 2 460101", "460101 3 153367", "153367 103 1489", "1489 1489 1" ]

3300009

3 71 15493

[ "3300009 3 1100003", "1100003 71 15493", "15493 15493 1" ]

2521244

2 2 11 57301

[ "2521244 2 1260622", "1260622 2 630311", "630311 11 57301", "57301 57301 1" ]

1948689

3 3 41 5281

[ "1948689 3 649563", "649563 3 216521", "216521 41 5281", "5281 5281 1" ]

929669

13 13 5501

[ "929669 13 71513", "71513 13 5501", "5501 5501 1" ]

805784

2 2 2 7 14389

[ "805784 2 402892", "402892 2 201446", "201446 2 100723", "100723 7 14389", "14389 14389 1" ]

4844455

5 7 11 12583

[ "4844455 5 968891", "968891 7 138413", "138413 11 12583", "12583 12583 1" ]

223630

2 5 11 19 107

[ "223630 2 111815", "111815 5 22363", "22363 11 2033", "2033 19 107", "107 107 1" ]

2123555

5 7 17 43 83

[ "2123555 5 424711", "424711 7 60673", "60673 17 3569", "3569 43 83", "83 83 1" ]

1244308

2 2 13 23929

[ "1244308 2 622154", "622154 2 311077", "311077 13 23929", "23929 23929 1" ]

3611027

7 515861

[ "3611027 7 515861", "515861 515861 1" ]

1308406

2 11 59473

[ "1308406 2 654203", "654203 11 59473", "59473 59473 1" ]

4231047

3 233 6053

[ "4231047 3 1410349", "1410349 233 6053", "6053 6053 1" ]

3982769

7 7 81281

[ "3982769 7 568967", "568967 7 81281", "81281 81281 1" ]

3753490

2 5 13 13 2221

[ "3753490 2 1876745", "1876745 5 375349", "375349 13 28873", "28873 13 2221", "2221 2221 1" ]

3257938

2 43 43 881

[ "3257938 2 1628969", "1628969 43 37883", "37883 43 881", "881 881 1" ]

3713876

2 2 928469

[ "3713876 2 1856938", "1856938 2 928469", "928469 928469 1" ]

3922891

7 7 7 11437

[ "3922891 7 560413", "560413 7 80059", "80059 7 11437", "11437 11437 1" ]

1148815

5 229763

[ "1148815 5 229763", "229763 229763 1" ]

535840

2 2 2 2 2 5 17 197

[ "535840 2 267920", "267920 2 133960", "133960 2 66980", "66980 2 33490", "33490 2 16745", "16745 5 3349", "3349 17 197", "197 197 1" ]

268085

5 53617

[ "268085 5 53617", "53617 53617 1" ]

1791269

[ "1791269 1791269 1" ]

1432521

3 3 159169

[ "1432521 3 477507", "477507 3 159169", "159169 159169 1" ]

363663

3 3 3 13469

[ "363663 3 121221", "121221 3 40407", "40407 3 13469", "13469 13469 1" ]

2278011

3 43 17659

[ "2278011 3 759337", "759337 43 17659", "17659 17659 1" ]

2403038

2 11 109229

[ "2403038 2 1201519", "1201519 11 109229", "109229 109229 1" ]

142606

2 113 631

[ "142606 2 71303", "71303 113 631", "631 631 1" ]

1136018

2 13 13 3361

[ "1136018 2 568009", "568009 13 43693", "43693 13 3361", "3361 3361 1" ]

4866946

2 7 41 61 139

[ "4866946 2 2433473", "2433473 7 347639", "347639 41 8479", "8479 61 139", "139 139 1" ]

127261

[ "127261 127261 1" ]

748792

2 2 2 11 67 127

[ "748792 2 374396", "374396 2 187198", "187198 2 93599", "93599 11 8509", "8509 67 127", "127 127 1" ]

4970865

3 5 331391

[ "4970865 3 1656955", "1656955 5 331391", "331391 331391 1" ]

138173

7 19739

[ "138173 7 19739", "19739 19739 1" ]

1852396

2 2 7 7 13 727

[ "1852396 2 926198", "926198 2 463099", "463099 7 66157", "66157 7 9451", "9451 13 727", "727 727 1" ]

457489

79 5791

[ "457489 79 5791", "5791 5791 1" ]

1702763

47 36229

[ "1702763 47 36229", "36229 36229 1" ]

3190142

2 1595071

[ "3190142 2 1595071", "1595071 1595071 1" ]

671016

2 2 2 3 73 383

[ "671016 2 335508", "335508 2 167754", "167754 2 83877", "83877 3 27959", "27959 73 383", "383 383 1" ]

233863

7 33409

[ "233863 7 33409", "33409 33409 1" ]

4793866

2 7 7 11 4447

[ "4793866 2 2396933", "2396933 7 342419", "342419 7 48917", "48917 11 4447", "4447 4447 1" ]

4052926

2 2026463

[ "4052926 2 2026463", "2026463 2026463 1" ]

1436662

2 718331

[ "1436662 2 718331", "718331 718331 1" ]

1772162

2 7 126583

[ "1772162 2 886081", "886081 7 126583", "126583 126583 1" ]

1919737

31 61927

[ "1919737 31 61927", "61927 61927 1" ]

227917

59 3863

[ "227917 59 3863", "3863 3863 1" ]

4330311

3 1443437

[ "4330311 3 1443437", "1443437 1443437 1" ]

4090606

2 13 131 1201

[ "4090606 2 2045303", "2045303 13 157331", "157331 131 1201", "1201 1201 1" ]

4045045

5 823 983

[ "4045045 5 809009", "809009 823 983", "983 983 1" ]

3659915

5 7 53 1973

[ "3659915 5 731983", "731983 7 104569", "104569 53 1973", "1973 1973 1" ]

3252169

[ "3252169 3252169 1" ]

133403

[ "133403 133403 1" ]

489094

2 244547

[ "489094 2 244547", "244547 244547 1" ]

90462

2 3 15077

[ "90462 2 45231", "45231 3 15077", "15077 15077 1" ]

1847047

19 97213

[ "1847047 19 97213", "97213 97213 1" ]

4619998

2 2309999

[ "4619998 2 2309999", "2309999 2309999 1" ]

4412005

5 13 103 659

[ "4412005 5 882401", "882401 13 67877", "67877 103 659", "659 659 1" ]