yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
222490	2 5 19 1171	[ "222490 2 111245", "111245 5 22249", "22249 19 1171", "1171 1171 1" ]
1619331	3 7 29 2659	[ "1619331 3 539777", "539777 7 77111", "77111 29 2659", "2659 2659 1" ]
2189386	2 1094693	[ "2189386 2 1094693", "1094693 1094693 1" ]
77492	2 2 19373	[ "77492 2 38746", "38746 2 19373", "19373 19373 1" ]
3701589	3 29 157 271	[ "3701589 3 1233863", "1233863 29 42547", "42547 157 271", "271 271 1" ]
2915746	2 1457873	[ "2915746 2 1457873", "1457873 1457873 1" ]
2717411	2717411	[ "2717411 2717411 1" ]
162887	19 8573	[ "162887 19 8573", "8573 8573 1" ]
3808434	2 3 7 90677	[ "3808434 2 1904217", "1904217 3 634739", "634739 7 90677", "90677 90677 1" ]
4107113	251 16363	[ "4107113 251 16363", "16363 16363 1" ]
4027218	2 3 13 51631	[ "4027218 2 2013609", "2013609 3 671203", "671203 13 51631", "51631 51631 1" ]
2740517	13 210809	[ "2740517 13 210809", "210809 210809 1" ]
1774453	1774453	[ "1774453 1774453 1" ]
3265606	2 19 19 4523	[ "3265606 2 1632803", "1632803 19 85937", "85937 19 4523", "4523 4523 1" ]
3006867	3 1002289	[ "3006867 3 1002289", "1002289 1002289 1" ]
1477903	7 211129	[ "1477903 7 211129", "211129 211129 1" ]
4971834	2 3 3 3 7 7 1879	[ "4971834 2 2485917", "2485917 3 828639", "828639 3 276213", "276213 3 92071", "92071 7 13153", "13153 7 1879", "1879 1879 1" ]
4377626	2 11 193 1031	[ "4377626 2 2188813", "2188813 11 198983", "198983 193 1031", "1031 1031 1" ]
957641	957641	[ "957641 957641 1" ]
4897919	13 23 16381	[ "4897919 13 376763", "376763 23 16381", "16381 16381 1" ]
890259	3 296753	[ "890259 3 296753", "296753 296753 1" ]
2214133	79 28027	[ "2214133 79 28027", "28027 28027 1" ]
1830907	13 140839	[ "1830907 13 140839", "140839 140839 1" ]
3335106	2 3 37 83 181	[ "3335106 2 1667553", "1667553 3 555851", "555851 37 15023", "15023 83 181", "181 181 1" ]
4517280	2 2 2 2 2 3 3 5 3137	[ "4517280 2 2258640", "2258640 2 1129320", "1129320 2 564660", "564660 2 282330", "282330 2 141165", "141165 3 47055", "47055 3 15685", "15685 5 3137", "3137 3137 1" ]
1763473	43 41011	[ "1763473 43 41011", "41011 41011 1" ]
3296626	2 37 44549	[ "3296626 2 1648313", "1648313 37 44549", "44549 44549 1" ]
458101	7 7 9349	[ "458101 7 65443", "65443 7 9349", "9349 9349 1" ]
3885	3 5 7 37	[ "3885 3 1295", "1295 5 259", "259 7 37", "37 37 1" ]
2158999	2158999	[ "2158999 2158999 1" ]
3807641	137 27793	[ "3807641 137 27793", "27793 27793 1" ]
1806503	1806503	[ "1806503 1806503 1" ]
4592658	2 3 7 43 2543	[ "4592658 2 2296329", "2296329 3 765443", "765443 7 109349", "109349 43 2543", "2543 2543 1" ]
671375	5 5 5 41 131	[ "671375 5 134275", "134275 5 26855", "26855 5 5371", "5371 41 131", "131 131 1" ]
3967189	3967189	[ "3967189 3967189 1" ]
2825746	2 7 11 59 311	[ "2825746 2 1412873", "1412873 7 201839", "201839 11 18349", "18349 59 311", "311 311 1" ]
765593	41 71 263	[ "765593 41 18673", "18673 71 263", "263 263 1" ]
1012019	83 89 137	[ "1012019 83 12193", "12193 89 137", "137 137 1" ]
1155431	1155431	[ "1155431 1155431 1" ]
3261444	2 2 3 271787	[ "3261444 2 1630722", "1630722 2 815361", "815361 3 271787", "271787 271787 1" ]
3781599	3 17 74149	[ "3781599 3 1260533", "1260533 17 74149", "74149 74149 1" ]
3323860	2 2 5 19 8747	[ "3323860 2 1661930", "1661930 2 830965", "830965 5 166193", "166193 19 8747", "8747 8747 1" ]
4299675	3 5 5 57329	[ "4299675 3 1433225", "1433225 5 286645", "286645 5 57329", "57329 57329 1" ]
3162747	3 7 150607	[ "3162747 3 1054249", "1054249 7 150607", "150607 150607 1" ]
285680	2 2 2 2 5 3571	[ "285680 2 142840", "142840 2 71420", "71420 2 35710", "35710 2 17855", "17855 5 3571", "3571 3571 1" ]
3732076	2 2 933019	[ "3732076 2 1866038", "1866038 2 933019", "933019 933019 1" ]
255404	2 2 67 953	[ "255404 2 127702", "127702 2 63851", "63851 67 953", "953 953 1" ]
272161	127 2143	[ "272161 127 2143", "2143 2143 1" ]
3555603	3 3 3 19 29 239	[ "3555603 3 1185201", "1185201 3 395067", "395067 3 131689", "131689 19 6931", "6931 29 239", "239 239 1" ]
959893	11 11 7933	[ "959893 11 87263", "87263 11 7933", "7933 7933 1" ]
1349669	1349669	[ "1349669 1349669 1" ]
777434	2 7 7 7933	[ "777434 2 388717", "388717 7 55531", "55531 7 7933", "7933 7933 1" ]
2195914	2 7 109 1439	[ "2195914 2 1097957", "1097957 7 156851", "156851 109 1439", "1439 1439 1" ]
2857818	2 3 67 7109	[ "2857818 2 1428909", "1428909 3 476303", "476303 67 7109", "7109 7109 1" ]
4142127	3 11 31 4049	[ "4142127 3 1380709", "1380709 11 125519", "125519 31 4049", "4049 4049 1" ]
4792098	2 3 59 13537	[ "4792098 2 2396049", "2396049 3 798683", "798683 59 13537", "13537 13537 1" ]
4461908	2 2 11 23 4409	[ "4461908 2 2230954", "2230954 2 1115477", "1115477 11 101407", "101407 23 4409", "4409 4409 1" ]
1462321	7 317 659	[ "1462321 7 208903", "208903 317 659", "659 659 1" ]
3187209	3 107 9929	[ "3187209 3 1062403", "1062403 107 9929", "9929 9929 1" ]
1006767	3 3 111863	[ "1006767 3 335589", "335589 3 111863", "111863 111863 1" ]
3704376	2 2 2 3 13 31 383	[ "3704376 2 1852188", "1852188 2 926094", "926094 2 463047", "463047 3 154349", "154349 13 11873", "11873 31 383", "383 383 1" ]
3873091	3873091	[ "3873091 3873091 1" ]
4297088	2 2 2 2 2 2 2 59 569	[ "4297088 2 2148544", "2148544 2 1074272", "1074272 2 537136", "537136 2 268568", "268568 2 134284", "134284 2 67142", "67142 2 33571", "33571 59 569", "569 569 1" ]
525421	13 13 3109	[ "525421 13 40417", "40417 13 3109", "3109 3109 1" ]
1044912	2 2 2 2 3 11 1979	[ "1044912 2 522456", "522456 2 261228", "261228 2 130614", "130614 2 65307", "65307 3 21769", "21769 11 1979", "1979 1979 1" ]
3042673	313 9721	[ "3042673 313 9721", "9721 9721 1" ]
3977679	3 97 13669	[ "3977679 3 1325893", "1325893 97 13669", "13669 13669 1" ]
1080223	1080223	[ "1080223 1080223 1" ]
3782178	2 3 3 19 11059	[ "3782178 2 1891089", "1891089 3 630363", "630363 3 210121", "210121 19 11059", "11059 11059 1" ]
2290974	2 3 7 54547	[ "2290974 2 1145487", "1145487 3 381829", "381829 7 54547", "54547 54547 1" ]
1939671	3 3 127 1697	[ "1939671 3 646557", "646557 3 215519", "215519 127 1697", "1697 1697 1" ]
1470526	2 735263	[ "1470526 2 735263", "735263 735263 1" ]
402691	402691	[ "402691 402691 1" ]
918809	31 107 277	[ "918809 31 29639", "29639 107 277", "277 277 1" ]
3095478	2 3 3 23 7477	[ "3095478 2 1547739", "1547739 3 515913", "515913 3 171971", "171971 23 7477", "7477 7477 1" ]
1597431	3 11 48407	[ "1597431 3 532477", "532477 11 48407", "48407 48407 1" ]
3231987	3 11 37 2647	[ "3231987 3 1077329", "1077329 11 97939", "97939 37 2647", "2647 2647 1" ]
1759282	2 7 53 2371	[ "1759282 2 879641", "879641 7 125663", "125663 53 2371", "2371 2371 1" ]
1217975	5 5 11 43 103	[ "1217975 5 243595", "243595 5 48719", "48719 11 4429", "4429 43 103", "103 103 1" ]
4824856	2 2 2 61 9887	[ "4824856 2 2412428", "2412428 2 1206214", "1206214 2 603107", "603107 61 9887", "9887 9887 1" ]
1135634	2 17 127 263	[ "1135634 2 567817", "567817 17 33401", "33401 127 263", "263 263 1" ]
4354080	2 2 2 2 2 3 5 47 193	[ "4354080 2 2177040", "2177040 2 1088520", "1088520 2 544260", "544260 2 272130", "272130 2 136065", "136065 3 45355", "45355 5 9071", "9071 47 193", "193 193 1" ]
1383237	3 3 3 3 17077	[ "1383237 3 461079", "461079 3 153693", "153693 3 51231", "51231 3 17077", "17077 17077 1" ]
3315675	3 5 5 11 4019	[ "3315675 3 1105225", "1105225 5 221045", "221045 5 44209", "44209 11 4019", "4019 4019 1" ]
1539808	2 2 2 2 2 48119	[ "1539808 2 769904", "769904 2 384952", "384952 2 192476", "192476 2 96238", "96238 2 48119", "48119 48119 1" ]
4974591	3 17 103 947	[ "4974591 3 1658197", "1658197 17 97541", "97541 103 947", "947 947 1" ]
1432414	2 83 8629	[ "1432414 2 716207", "716207 83 8629", "8629 8629 1" ]
4492223	61 73643	[ "4492223 61 73643", "73643 73643 1" ]
766651	766651	[ "766651 766651 1" ]
1672983	3 3 13 79 181	[ "1672983 3 557661", "557661 3 185887", "185887 13 14299", "14299 79 181", "181 181 1" ]
1674411	3 433 1289	[ "1674411 3 558137", "558137 433 1289", "1289 1289 1" ]
3238910	2 5 157 2063	[ "3238910 2 1619455", "1619455 5 323891", "323891 157 2063", "2063 2063 1" ]
2100240	2 2 2 2 3 3 5 2917	[ "2100240 2 1050120", "1050120 2 525060", "525060 2 262530", "262530 2 131265", "131265 3 43755", "43755 3 14585", "14585 5 2917", "2917 2917 1" ]
887554	2 443777	[ "887554 2 443777", "443777 443777 1" ]
4602428	2 2 47 24481	[ "4602428 2 2301214", "2301214 2 1150607", "1150607 47 24481", "24481 24481 1" ]
925709	29 137 233	[ "925709 29 31921", "31921 137 233", "233 233 1" ]
1495374	2 3 249229	[ "1495374 2 747687", "747687 3 249229", "249229 249229 1" ]
3730604	2 2 932651	[ "3730604 2 1865302", "1865302 2 932651", "932651 932651 1" ]
2824291	2824291	[ "2824291 2824291 1" ]
4839317	7 29 31 769	[ "4839317 7 691331", "691331 29 23839", "23839 31 769", "769 769 1" ]

222490

2 5 19 1171

[ "222490 2 111245", "111245 5 22249", "22249 19 1171", "1171 1171 1" ]

1619331

3 7 29 2659

[ "1619331 3 539777", "539777 7 77111", "77111 29 2659", "2659 2659 1" ]

2189386

2 1094693

[ "2189386 2 1094693", "1094693 1094693 1" ]

77492

2 2 19373

[ "77492 2 38746", "38746 2 19373", "19373 19373 1" ]

3701589

3 29 157 271

[ "3701589 3 1233863", "1233863 29 42547", "42547 157 271", "271 271 1" ]

2915746

2 1457873

[ "2915746 2 1457873", "1457873 1457873 1" ]

2717411

[ "2717411 2717411 1" ]

162887

19 8573

[ "162887 19 8573", "8573 8573 1" ]

3808434

2 3 7 90677

[ "3808434 2 1904217", "1904217 3 634739", "634739 7 90677", "90677 90677 1" ]

4107113

251 16363

[ "4107113 251 16363", "16363 16363 1" ]

4027218

2 3 13 51631

[ "4027218 2 2013609", "2013609 3 671203", "671203 13 51631", "51631 51631 1" ]

2740517

13 210809

[ "2740517 13 210809", "210809 210809 1" ]

1774453

[ "1774453 1774453 1" ]

3265606

2 19 19 4523

[ "3265606 2 1632803", "1632803 19 85937", "85937 19 4523", "4523 4523 1" ]

3006867

3 1002289

[ "3006867 3 1002289", "1002289 1002289 1" ]

1477903

7 211129

[ "1477903 7 211129", "211129 211129 1" ]

4971834

2 3 3 3 7 7 1879

[ "4971834 2 2485917", "2485917 3 828639", "828639 3 276213", "276213 3 92071", "92071 7 13153", "13153 7 1879", "1879 1879 1" ]

4377626

2 11 193 1031

[ "4377626 2 2188813", "2188813 11 198983", "198983 193 1031", "1031 1031 1" ]

957641

[ "957641 957641 1" ]

4897919

13 23 16381

[ "4897919 13 376763", "376763 23 16381", "16381 16381 1" ]

890259

3 296753

[ "890259 3 296753", "296753 296753 1" ]

2214133

79 28027

[ "2214133 79 28027", "28027 28027 1" ]

1830907

13 140839

[ "1830907 13 140839", "140839 140839 1" ]

3335106

2 3 37 83 181

[ "3335106 2 1667553", "1667553 3 555851", "555851 37 15023", "15023 83 181", "181 181 1" ]

4517280

2 2 2 2 2 3 3 5 3137

[ "4517280 2 2258640", "2258640 2 1129320", "1129320 2 564660", "564660 2 282330", "282330 2 141165", "141165 3 47055", "47055 3 15685", "15685 5 3137", "3137 3137 1" ]

1763473

43 41011

[ "1763473 43 41011", "41011 41011 1" ]

3296626

2 37 44549

[ "3296626 2 1648313", "1648313 37 44549", "44549 44549 1" ]

458101

7 7 9349

[ "458101 7 65443", "65443 7 9349", "9349 9349 1" ]

3885

3 5 7 37

[ "3885 3 1295", "1295 5 259", "259 7 37", "37 37 1" ]

2158999

[ "2158999 2158999 1" ]

3807641

137 27793

[ "3807641 137 27793", "27793 27793 1" ]

1806503

[ "1806503 1806503 1" ]

4592658

2 3 7 43 2543

[ "4592658 2 2296329", "2296329 3 765443", "765443 7 109349", "109349 43 2543", "2543 2543 1" ]

671375

5 5 5 41 131

[ "671375 5 134275", "134275 5 26855", "26855 5 5371", "5371 41 131", "131 131 1" ]

3967189

[ "3967189 3967189 1" ]

2825746

2 7 11 59 311

[ "2825746 2 1412873", "1412873 7 201839", "201839 11 18349", "18349 59 311", "311 311 1" ]

765593

41 71 263

[ "765593 41 18673", "18673 71 263", "263 263 1" ]

1012019

83 89 137

[ "1012019 83 12193", "12193 89 137", "137 137 1" ]

1155431

[ "1155431 1155431 1" ]

3261444

2 2 3 271787

[ "3261444 2 1630722", "1630722 2 815361", "815361 3 271787", "271787 271787 1" ]

3781599

3 17 74149

[ "3781599 3 1260533", "1260533 17 74149", "74149 74149 1" ]

3323860

2 2 5 19 8747

[ "3323860 2 1661930", "1661930 2 830965", "830965 5 166193", "166193 19 8747", "8747 8747 1" ]

4299675

3 5 5 57329

[ "4299675 3 1433225", "1433225 5 286645", "286645 5 57329", "57329 57329 1" ]

3162747

3 7 150607

[ "3162747 3 1054249", "1054249 7 150607", "150607 150607 1" ]

285680

2 2 2 2 5 3571

[ "285680 2 142840", "142840 2 71420", "71420 2 35710", "35710 2 17855", "17855 5 3571", "3571 3571 1" ]

3732076

2 2 933019

[ "3732076 2 1866038", "1866038 2 933019", "933019 933019 1" ]

255404

2 2 67 953

[ "255404 2 127702", "127702 2 63851", "63851 67 953", "953 953 1" ]

272161

127 2143

[ "272161 127 2143", "2143 2143 1" ]

3555603

3 3 3 19 29 239

[ "3555603 3 1185201", "1185201 3 395067", "395067 3 131689", "131689 19 6931", "6931 29 239", "239 239 1" ]

959893

11 11 7933

[ "959893 11 87263", "87263 11 7933", "7933 7933 1" ]

1349669

[ "1349669 1349669 1" ]

777434

2 7 7 7933

[ "777434 2 388717", "388717 7 55531", "55531 7 7933", "7933 7933 1" ]

2195914

2 7 109 1439

[ "2195914 2 1097957", "1097957 7 156851", "156851 109 1439", "1439 1439 1" ]

2857818

2 3 67 7109

[ "2857818 2 1428909", "1428909 3 476303", "476303 67 7109", "7109 7109 1" ]

4142127

3 11 31 4049

[ "4142127 3 1380709", "1380709 11 125519", "125519 31 4049", "4049 4049 1" ]

4792098

2 3 59 13537

[ "4792098 2 2396049", "2396049 3 798683", "798683 59 13537", "13537 13537 1" ]

4461908

2 2 11 23 4409

[ "4461908 2 2230954", "2230954 2 1115477", "1115477 11 101407", "101407 23 4409", "4409 4409 1" ]

1462321

7 317 659

[ "1462321 7 208903", "208903 317 659", "659 659 1" ]

3187209

3 107 9929

[ "3187209 3 1062403", "1062403 107 9929", "9929 9929 1" ]

1006767

3 3 111863

[ "1006767 3 335589", "335589 3 111863", "111863 111863 1" ]

3704376

2 2 2 3 13 31 383

[ "3704376 2 1852188", "1852188 2 926094", "926094 2 463047", "463047 3 154349", "154349 13 11873", "11873 31 383", "383 383 1" ]

3873091

[ "3873091 3873091 1" ]

4297088

2 2 2 2 2 2 2 59 569

[ "4297088 2 2148544", "2148544 2 1074272", "1074272 2 537136", "537136 2 268568", "268568 2 134284", "134284 2 67142", "67142 2 33571", "33571 59 569", "569 569 1" ]

525421

13 13 3109

[ "525421 13 40417", "40417 13 3109", "3109 3109 1" ]

1044912

2 2 2 2 3 11 1979

[ "1044912 2 522456", "522456 2 261228", "261228 2 130614", "130614 2 65307", "65307 3 21769", "21769 11 1979", "1979 1979 1" ]

3042673

313 9721

[ "3042673 313 9721", "9721 9721 1" ]

3977679

3 97 13669

[ "3977679 3 1325893", "1325893 97 13669", "13669 13669 1" ]

1080223

[ "1080223 1080223 1" ]

3782178

2 3 3 19 11059

[ "3782178 2 1891089", "1891089 3 630363", "630363 3 210121", "210121 19 11059", "11059 11059 1" ]

2290974

2 3 7 54547

[ "2290974 2 1145487", "1145487 3 381829", "381829 7 54547", "54547 54547 1" ]

1939671

3 3 127 1697

[ "1939671 3 646557", "646557 3 215519", "215519 127 1697", "1697 1697 1" ]

1470526

2 735263

[ "1470526 2 735263", "735263 735263 1" ]

402691

[ "402691 402691 1" ]

918809

31 107 277

[ "918809 31 29639", "29639 107 277", "277 277 1" ]

3095478

2 3 3 23 7477

[ "3095478 2 1547739", "1547739 3 515913", "515913 3 171971", "171971 23 7477", "7477 7477 1" ]

1597431

3 11 48407

[ "1597431 3 532477", "532477 11 48407", "48407 48407 1" ]

3231987

3 11 37 2647

[ "3231987 3 1077329", "1077329 11 97939", "97939 37 2647", "2647 2647 1" ]

1759282

2 7 53 2371

[ "1759282 2 879641", "879641 7 125663", "125663 53 2371", "2371 2371 1" ]

1217975

5 5 11 43 103

[ "1217975 5 243595", "243595 5 48719", "48719 11 4429", "4429 43 103", "103 103 1" ]

4824856

2 2 2 61 9887

[ "4824856 2 2412428", "2412428 2 1206214", "1206214 2 603107", "603107 61 9887", "9887 9887 1" ]

1135634

2 17 127 263

[ "1135634 2 567817", "567817 17 33401", "33401 127 263", "263 263 1" ]

4354080

2 2 2 2 2 3 5 47 193

[ "4354080 2 2177040", "2177040 2 1088520", "1088520 2 544260", "544260 2 272130", "272130 2 136065", "136065 3 45355", "45355 5 9071", "9071 47 193", "193 193 1" ]

1383237

3 3 3 3 17077

[ "1383237 3 461079", "461079 3 153693", "153693 3 51231", "51231 3 17077", "17077 17077 1" ]

3315675

3 5 5 11 4019

[ "3315675 3 1105225", "1105225 5 221045", "221045 5 44209", "44209 11 4019", "4019 4019 1" ]

1539808

2 2 2 2 2 48119

[ "1539808 2 769904", "769904 2 384952", "384952 2 192476", "192476 2 96238", "96238 2 48119", "48119 48119 1" ]

4974591

3 17 103 947

[ "4974591 3 1658197", "1658197 17 97541", "97541 103 947", "947 947 1" ]

1432414

2 83 8629

[ "1432414 2 716207", "716207 83 8629", "8629 8629 1" ]

4492223

61 73643

[ "4492223 61 73643", "73643 73643 1" ]

766651

[ "766651 766651 1" ]

1672983

3 3 13 79 181

[ "1672983 3 557661", "557661 3 185887", "185887 13 14299", "14299 79 181", "181 181 1" ]

1674411

3 433 1289

[ "1674411 3 558137", "558137 433 1289", "1289 1289 1" ]

3238910

2 5 157 2063

[ "3238910 2 1619455", "1619455 5 323891", "323891 157 2063", "2063 2063 1" ]

2100240

2 2 2 2 3 3 5 2917

[ "2100240 2 1050120", "1050120 2 525060", "525060 2 262530", "262530 2 131265", "131265 3 43755", "43755 3 14585", "14585 5 2917", "2917 2917 1" ]

887554

2 443777

[ "887554 2 443777", "443777 443777 1" ]

4602428

2 2 47 24481

[ "4602428 2 2301214", "2301214 2 1150607", "1150607 47 24481", "24481 24481 1" ]

925709

29 137 233

[ "925709 29 31921", "31921 137 233", "233 233 1" ]

1495374

2 3 249229

[ "1495374 2 747687", "747687 3 249229", "249229 249229 1" ]

3730604

2 2 932651

[ "3730604 2 1865302", "1865302 2 932651", "932651 932651 1" ]

2824291

[ "2824291 2824291 1" ]

4839317

7 29 31 769

[ "4839317 7 691331", "691331 29 23839", "23839 31 769", "769 769 1" ]