yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
2512705	5 13 29 31 43	[ "2512705 5 502541", "502541 13 38657", "38657 29 1333", "1333 31 43", "43 43 1" ]
2280803	7 7 89 523	[ "2280803 7 325829", "325829 7 46547", "46547 89 523", "523 523 1" ]
295650	2 3 3 3 3 5 5 73	[ "295650 2 147825", "147825 3 49275", "49275 3 16425", "16425 3 5475", "5475 3 1825", "1825 5 365", "365 5 73", "73 73 1" ]
727154	2 363577	[ "727154 2 363577", "363577 363577 1" ]
3351988	2 2 101 8297	[ "3351988 2 1675994", "1675994 2 837997", "837997 101 8297", "8297 8297 1" ]
498013	498013	[ "498013 498013 1" ]
1342088	2 2 2 11 101 151	[ "1342088 2 671044", "671044 2 335522", "335522 2 167761", "167761 11 15251", "15251 101 151", "151 151 1" ]
2187188	2 2 353 1549	[ "2187188 2 1093594", "1093594 2 546797", "546797 353 1549", "1549 1549 1" ]
4320386	2 7 61 5059	[ "4320386 2 2160193", "2160193 7 308599", "308599 61 5059", "5059 5059 1" ]
4375854	2 3 3 7 34729	[ "4375854 2 2187927", "2187927 3 729309", "729309 3 243103", "243103 7 34729", "34729 34729 1" ]
2391035	5 478207	[ "2391035 5 478207", "478207 478207 1" ]
1096623	3 3 11 11 19 53	[ "1096623 3 365541", "365541 3 121847", "121847 11 11077", "11077 11 1007", "1007 19 53", "53 53 1" ]
267939	3 3 7 4253	[ "267939 3 89313", "89313 3 29771", "29771 7 4253", "4253 4253 1" ]
171947	171947	[ "171947 171947 1" ]
311802	2 3 157 331	[ "311802 2 155901", "155901 3 51967", "51967 157 331", "331 331 1" ]
2214390	2 3 5 223 331	[ "2214390 2 1107195", "1107195 3 369065", "369065 5 73813", "73813 223 331", "331 331 1" ]
956740	2 2 5 47837	[ "956740 2 478370", "478370 2 239185", "239185 5 47837", "47837 47837 1" ]
3229255	5 645851	[ "3229255 5 645851", "645851 645851 1" ]
874873	874873	[ "874873 874873 1" ]
1637339	11 47 3167	[ "1637339 11 148849", "148849 47 3167", "3167 3167 1" ]
3289139	7 469877	[ "3289139 7 469877", "469877 469877 1" ]
1389781	67 20743	[ "1389781 67 20743", "20743 20743 1" ]
1478518	2 61 12119	[ "1478518 2 739259", "739259 61 12119", "12119 12119 1" ]
2464854	2 3 7 58687	[ "2464854 2 1232427", "1232427 3 410809", "410809 7 58687", "58687 58687 1" ]
3465743	3465743	[ "3465743 3465743 1" ]
75070	2 5 7507	[ "75070 2 37535", "37535 5 7507", "7507 7507 1" ]
1024376	2 2 2 128047	[ "1024376 2 512188", "512188 2 256094", "256094 2 128047", "128047 128047 1" ]
1732410	2 3 3 5 19249	[ "1732410 2 866205", "866205 3 288735", "288735 3 96245", "96245 5 19249", "19249 19249 1" ]
3629238	2 3 41 14753	[ "3629238 2 1814619", "1814619 3 604873", "604873 41 14753", "14753 14753 1" ]
1445670	2 3 3 5 16063	[ "1445670 2 722835", "722835 3 240945", "240945 3 80315", "80315 5 16063", "16063 16063 1" ]
621449	73 8513	[ "621449 73 8513", "8513 8513 1" ]
4783033	73 65521	[ "4783033 73 65521", "65521 65521 1" ]
2207769	3 191 3853	[ "2207769 3 735923", "735923 191 3853", "3853 3853 1" ]
4699722	2 3 53 14779	[ "4699722 2 2349861", "2349861 3 783287", "783287 53 14779", "14779 14779 1" ]
2183433	3 7 173 601	[ "2183433 3 727811", "727811 7 103973", "103973 173 601", "601 601 1" ]
1976451	3 658817	[ "1976451 3 658817", "658817 658817 1" ]
3087666	2 3 3 3 57179	[ "3087666 2 1543833", "1543833 3 514611", "514611 3 171537", "171537 3 57179", "57179 57179 1" ]
4205754	2 3 3 7 29 1151	[ "4205754 2 2102877", "2102877 3 700959", "700959 3 233653", "233653 7 33379", "33379 29 1151", "1151 1151 1" ]
4980320	2 2 2 2 2 5 17 1831	[ "4980320 2 2490160", "2490160 2 1245080", "1245080 2 622540", "622540 2 311270", "311270 2 155635", "155635 5 31127", "31127 17 1831", "1831 1831 1" ]
2000580	2 2 3 5 33343	[ "2000580 2 1000290", "1000290 2 500145", "500145 3 166715", "166715 5 33343", "33343 33343 1" ]
4899931	4899931	[ "4899931 4899931 1" ]
2642106	2 3 17 25903	[ "2642106 2 1321053", "1321053 3 440351", "440351 17 25903", "25903 25903 1" ]
2609943	3 7 37 3359	[ "2609943 3 869981", "869981 7 124283", "124283 37 3359", "3359 3359 1" ]
4309796	2 2 1077449	[ "4309796 2 2154898", "2154898 2 1077449", "1077449 1077449 1" ]
881802	2 3 3 48989	[ "881802 2 440901", "440901 3 146967", "146967 3 48989", "48989 48989 1" ]
1016329	19 149 359	[ "1016329 19 53491", "53491 149 359", "359 359 1" ]
254129	47 5407	[ "254129 47 5407", "5407 5407 1" ]
1619145	3 3 5 11 3271	[ "1619145 3 539715", "539715 3 179905", "179905 5 35981", "35981 11 3271", "3271 3271 1" ]
2372101	2372101	[ "2372101 2372101 1" ]
1242164	2 2 7 11 37 109	[ "1242164 2 621082", "621082 2 310541", "310541 7 44363", "44363 11 4033", "4033 37 109", "109 109 1" ]
456378	2 3 13 5851	[ "456378 2 228189", "228189 3 76063", "76063 13 5851", "5851 5851 1" ]
209981	59 3559	[ "209981 59 3559", "3559 3559 1" ]
1067735	5 179 1193	[ "1067735 5 213547", "213547 179 1193", "1193 1193 1" ]
1596725	5 5 13 17 17 17	[ "1596725 5 319345", "319345 5 63869", "63869 13 4913", "4913 17 289", "289 17 17", "17 17 1" ]
3977267	7 227 2503	[ "3977267 7 568181", "568181 227 2503", "2503 2503 1" ]
766729	71 10799	[ "766729 71 10799", "10799 10799 1" ]
1688359	19 88861	[ "1688359 19 88861", "88861 88861 1" ]
3887003	3887003	[ "3887003 3887003 1" ]
1410193	991 1423	[ "1410193 991 1423", "1423 1423 1" ]
469471	19 24709	[ "469471 19 24709", "24709 24709 1" ]
2333921	61 38261	[ "2333921 61 38261", "38261 38261 1" ]
168228	2 2 3 3 4673	[ "168228 2 84114", "84114 2 42057", "42057 3 14019", "14019 3 4673", "4673 4673 1" ]
1192637	103 11579	[ "1192637 103 11579", "11579 11579 1" ]
1362914	2 7 67 1453	[ "1362914 2 681457", "681457 7 97351", "97351 67 1453", "1453 1453 1" ]
4893183	3 3 3 127 1427	[ "4893183 3 1631061", "1631061 3 543687", "543687 3 181229", "181229 127 1427", "1427 1427 1" ]
1647156	2 2 3 7 19609	[ "1647156 2 823578", "823578 2 411789", "411789 3 137263", "137263 7 19609", "19609 19609 1" ]
1030095	3 3 5 11 2081	[ "1030095 3 343365", "343365 3 114455", "114455 5 22891", "22891 11 2081", "2081 2081 1" ]
296675	5 5 11867	[ "296675 5 59335", "59335 5 11867", "11867 11867 1" ]
1151905	5 101 2281	[ "1151905 5 230381", "230381 101 2281", "2281 2281 1" ]
1455708	2 2 3 121309	[ "1455708 2 727854", "727854 2 363927", "363927 3 121309", "121309 121309 1" ]
1300721	17 19 4027	[ "1300721 17 76513", "76513 19 4027", "4027 4027 1" ]
2623305	3 5 47 61 61	[ "2623305 3 874435", "874435 5 174887", "174887 47 3721", "3721 61 61", "61 61 1" ]
1832739	3 610913	[ "1832739 3 610913", "610913 610913 1" ]
1907109	3 3 313 677	[ "1907109 3 635703", "635703 3 211901", "211901 313 677", "677 677 1" ]
1735389	3 3 29 61 109	[ "1735389 3 578463", "578463 3 192821", "192821 29 6649", "6649 61 109", "109 109 1" ]
3250301	3250301	[ "3250301 3250301 1" ]
2607960	2 2 2 3 5 103 211	[ "2607960 2 1303980", "1303980 2 651990", "651990 2 325995", "325995 3 108665", "108665 5 21733", "21733 103 211", "211 211 1" ]
4803397	4803397	[ "4803397 4803397 1" ]
3098056	2 2 2 13 29789	[ "3098056 2 1549028", "1549028 2 774514", "774514 2 387257", "387257 13 29789", "29789 29789 1" ]
4038193	47 151 569	[ "4038193 47 85919", "85919 151 569", "569 569 1" ]
3925070	2 5 83 4729	[ "3925070 2 1962535", "1962535 5 392507", "392507 83 4729", "4729 4729 1" ]
1870127	7 433 617	[ "1870127 7 267161", "267161 433 617", "617 617 1" ]
1355282	2 173 3917	[ "1355282 2 677641", "677641 173 3917", "3917 3917 1" ]
4923796	2 2 1230949	[ "4923796 2 2461898", "2461898 2 1230949", "1230949 1230949 1" ]
3785984	2 2 2 2 2 2 2 2 23 643	[ "3785984 2 1892992", "1892992 2 946496", "946496 2 473248", "473248 2 236624", "236624 2 118312", "118312 2 59156", "59156 2 29578", "29578 2 14789", "14789 23 643", "643 643 1" ]
501219	3 3 55691	[ "501219 3 167073", "167073 3 55691", "55691 55691 1" ]
3819293	31 123203	[ "3819293 31 123203", "123203 123203 1" ]
3477954	2 3 449 1291	[ "3477954 2 1738977", "1738977 3 579659", "579659 449 1291", "1291 1291 1" ]
785792	2 2 2 2 2 2 2 7 877	[ "785792 2 392896", "392896 2 196448", "196448 2 98224", "98224 2 49112", "49112 2 24556", "24556 2 12278", "12278 2 6139", "6139 7 877", "877 877 1" ]
2755162	2 919 1499	[ "2755162 2 1377581", "1377581 919 1499", "1499 1499 1" ]
2867775	3 5 5 38237	[ "2867775 3 955925", "955925 5 191185", "191185 5 38237", "38237 38237 1" ]
3084341	13 237257	[ "3084341 13 237257", "237257 237257 1" ]
4183983	3 3 397 1171	[ "4183983 3 1394661", "1394661 3 464887", "464887 397 1171", "1171 1171 1" ]
1005734	2 37 13591	[ "1005734 2 502867", "502867 37 13591", "13591 13591 1" ]
2386871	23 157 661	[ "2386871 23 103777", "103777 157 661", "661 661 1" ]
1293865	5 23 11251	[ "1293865 5 258773", "258773 23 11251", "11251 11251 1" ]
1422845	5 383 743	[ "1422845 5 284569", "284569 383 743", "743 743 1" ]
1990373	7 11 25849	[ "1990373 7 284339", "284339 11 25849", "25849 25849 1" ]
3403096	2 2 2 425387	[ "3403096 2 1701548", "1701548 2 850774", "850774 2 425387", "425387 425387 1" ]
2810597	2810597	[ "2810597 2810597 1" ]

2512705

5 13 29 31 43

[ "2512705 5 502541", "502541 13 38657", "38657 29 1333", "1333 31 43", "43 43 1" ]

2280803

7 7 89 523

[ "2280803 7 325829", "325829 7 46547", "46547 89 523", "523 523 1" ]

295650

2 3 3 3 3 5 5 73

[ "295650 2 147825", "147825 3 49275", "49275 3 16425", "16425 3 5475", "5475 3 1825", "1825 5 365", "365 5 73", "73 73 1" ]

727154

2 363577

[ "727154 2 363577", "363577 363577 1" ]

3351988

2 2 101 8297

[ "3351988 2 1675994", "1675994 2 837997", "837997 101 8297", "8297 8297 1" ]

498013

[ "498013 498013 1" ]

1342088

2 2 2 11 101 151

[ "1342088 2 671044", "671044 2 335522", "335522 2 167761", "167761 11 15251", "15251 101 151", "151 151 1" ]

2187188

2 2 353 1549

[ "2187188 2 1093594", "1093594 2 546797", "546797 353 1549", "1549 1549 1" ]

4320386

2 7 61 5059

[ "4320386 2 2160193", "2160193 7 308599", "308599 61 5059", "5059 5059 1" ]

4375854

2 3 3 7 34729

[ "4375854 2 2187927", "2187927 3 729309", "729309 3 243103", "243103 7 34729", "34729 34729 1" ]

2391035

5 478207

[ "2391035 5 478207", "478207 478207 1" ]

1096623

3 3 11 11 19 53

[ "1096623 3 365541", "365541 3 121847", "121847 11 11077", "11077 11 1007", "1007 19 53", "53 53 1" ]

267939

3 3 7 4253

[ "267939 3 89313", "89313 3 29771", "29771 7 4253", "4253 4253 1" ]

171947

[ "171947 171947 1" ]

311802

2 3 157 331

[ "311802 2 155901", "155901 3 51967", "51967 157 331", "331 331 1" ]

2214390

2 3 5 223 331

[ "2214390 2 1107195", "1107195 3 369065", "369065 5 73813", "73813 223 331", "331 331 1" ]

956740

2 2 5 47837

[ "956740 2 478370", "478370 2 239185", "239185 5 47837", "47837 47837 1" ]

3229255

5 645851

[ "3229255 5 645851", "645851 645851 1" ]

874873

[ "874873 874873 1" ]

1637339

11 47 3167

[ "1637339 11 148849", "148849 47 3167", "3167 3167 1" ]

3289139

7 469877

[ "3289139 7 469877", "469877 469877 1" ]

1389781

67 20743

[ "1389781 67 20743", "20743 20743 1" ]

1478518

2 61 12119

[ "1478518 2 739259", "739259 61 12119", "12119 12119 1" ]

2464854

2 3 7 58687

[ "2464854 2 1232427", "1232427 3 410809", "410809 7 58687", "58687 58687 1" ]

3465743

[ "3465743 3465743 1" ]

75070

2 5 7507

[ "75070 2 37535", "37535 5 7507", "7507 7507 1" ]

1024376

2 2 2 128047

[ "1024376 2 512188", "512188 2 256094", "256094 2 128047", "128047 128047 1" ]

1732410

2 3 3 5 19249

[ "1732410 2 866205", "866205 3 288735", "288735 3 96245", "96245 5 19249", "19249 19249 1" ]

3629238

2 3 41 14753

[ "3629238 2 1814619", "1814619 3 604873", "604873 41 14753", "14753 14753 1" ]

1445670

2 3 3 5 16063

[ "1445670 2 722835", "722835 3 240945", "240945 3 80315", "80315 5 16063", "16063 16063 1" ]

621449

73 8513

[ "621449 73 8513", "8513 8513 1" ]

4783033

73 65521

[ "4783033 73 65521", "65521 65521 1" ]

2207769

3 191 3853

[ "2207769 3 735923", "735923 191 3853", "3853 3853 1" ]

4699722

2 3 53 14779

[ "4699722 2 2349861", "2349861 3 783287", "783287 53 14779", "14779 14779 1" ]

2183433

3 7 173 601

[ "2183433 3 727811", "727811 7 103973", "103973 173 601", "601 601 1" ]

1976451

3 658817

[ "1976451 3 658817", "658817 658817 1" ]

3087666

2 3 3 3 57179

[ "3087666 2 1543833", "1543833 3 514611", "514611 3 171537", "171537 3 57179", "57179 57179 1" ]

4205754

2 3 3 7 29 1151

[ "4205754 2 2102877", "2102877 3 700959", "700959 3 233653", "233653 7 33379", "33379 29 1151", "1151 1151 1" ]

4980320

2 2 2 2 2 5 17 1831

[ "4980320 2 2490160", "2490160 2 1245080", "1245080 2 622540", "622540 2 311270", "311270 2 155635", "155635 5 31127", "31127 17 1831", "1831 1831 1" ]

2000580

2 2 3 5 33343

[ "2000580 2 1000290", "1000290 2 500145", "500145 3 166715", "166715 5 33343", "33343 33343 1" ]

4899931

[ "4899931 4899931 1" ]

2642106

2 3 17 25903

[ "2642106 2 1321053", "1321053 3 440351", "440351 17 25903", "25903 25903 1" ]

2609943

3 7 37 3359

[ "2609943 3 869981", "869981 7 124283", "124283 37 3359", "3359 3359 1" ]

4309796

2 2 1077449

[ "4309796 2 2154898", "2154898 2 1077449", "1077449 1077449 1" ]

881802

2 3 3 48989

[ "881802 2 440901", "440901 3 146967", "146967 3 48989", "48989 48989 1" ]

1016329

19 149 359

[ "1016329 19 53491", "53491 149 359", "359 359 1" ]

254129

47 5407

[ "254129 47 5407", "5407 5407 1" ]

1619145

3 3 5 11 3271

[ "1619145 3 539715", "539715 3 179905", "179905 5 35981", "35981 11 3271", "3271 3271 1" ]

2372101

[ "2372101 2372101 1" ]

1242164

2 2 7 11 37 109

[ "1242164 2 621082", "621082 2 310541", "310541 7 44363", "44363 11 4033", "4033 37 109", "109 109 1" ]

456378

2 3 13 5851

[ "456378 2 228189", "228189 3 76063", "76063 13 5851", "5851 5851 1" ]

209981

59 3559

[ "209981 59 3559", "3559 3559 1" ]

1067735

5 179 1193

[ "1067735 5 213547", "213547 179 1193", "1193 1193 1" ]

1596725

5 5 13 17 17 17

[ "1596725 5 319345", "319345 5 63869", "63869 13 4913", "4913 17 289", "289 17 17", "17 17 1" ]

3977267

7 227 2503

[ "3977267 7 568181", "568181 227 2503", "2503 2503 1" ]

766729

71 10799

[ "766729 71 10799", "10799 10799 1" ]

1688359

19 88861

[ "1688359 19 88861", "88861 88861 1" ]

3887003

[ "3887003 3887003 1" ]

1410193

991 1423

[ "1410193 991 1423", "1423 1423 1" ]

469471

19 24709

[ "469471 19 24709", "24709 24709 1" ]

2333921

61 38261

[ "2333921 61 38261", "38261 38261 1" ]

168228

2 2 3 3 4673

[ "168228 2 84114", "84114 2 42057", "42057 3 14019", "14019 3 4673", "4673 4673 1" ]

1192637

103 11579

[ "1192637 103 11579", "11579 11579 1" ]

1362914

2 7 67 1453

[ "1362914 2 681457", "681457 7 97351", "97351 67 1453", "1453 1453 1" ]

4893183

3 3 3 127 1427

[ "4893183 3 1631061", "1631061 3 543687", "543687 3 181229", "181229 127 1427", "1427 1427 1" ]

1647156

2 2 3 7 19609

[ "1647156 2 823578", "823578 2 411789", "411789 3 137263", "137263 7 19609", "19609 19609 1" ]

1030095

3 3 5 11 2081

[ "1030095 3 343365", "343365 3 114455", "114455 5 22891", "22891 11 2081", "2081 2081 1" ]

296675

5 5 11867

[ "296675 5 59335", "59335 5 11867", "11867 11867 1" ]

1151905

5 101 2281

[ "1151905 5 230381", "230381 101 2281", "2281 2281 1" ]

1455708

2 2 3 121309

[ "1455708 2 727854", "727854 2 363927", "363927 3 121309", "121309 121309 1" ]

1300721

17 19 4027

[ "1300721 17 76513", "76513 19 4027", "4027 4027 1" ]

2623305

3 5 47 61 61

[ "2623305 3 874435", "874435 5 174887", "174887 47 3721", "3721 61 61", "61 61 1" ]

1832739

3 610913

[ "1832739 3 610913", "610913 610913 1" ]

1907109

3 3 313 677

[ "1907109 3 635703", "635703 3 211901", "211901 313 677", "677 677 1" ]

1735389

3 3 29 61 109

[ "1735389 3 578463", "578463 3 192821", "192821 29 6649", "6649 61 109", "109 109 1" ]

3250301

[ "3250301 3250301 1" ]

2607960

2 2 2 3 5 103 211

[ "2607960 2 1303980", "1303980 2 651990", "651990 2 325995", "325995 3 108665", "108665 5 21733", "21733 103 211", "211 211 1" ]

4803397

[ "4803397 4803397 1" ]

3098056

2 2 2 13 29789

[ "3098056 2 1549028", "1549028 2 774514", "774514 2 387257", "387257 13 29789", "29789 29789 1" ]

4038193

47 151 569

[ "4038193 47 85919", "85919 151 569", "569 569 1" ]

3925070

2 5 83 4729

[ "3925070 2 1962535", "1962535 5 392507", "392507 83 4729", "4729 4729 1" ]

1870127

7 433 617

[ "1870127 7 267161", "267161 433 617", "617 617 1" ]

1355282

2 173 3917

[ "1355282 2 677641", "677641 173 3917", "3917 3917 1" ]

4923796

2 2 1230949

[ "4923796 2 2461898", "2461898 2 1230949", "1230949 1230949 1" ]

3785984

2 2 2 2 2 2 2 2 23 643

[ "3785984 2 1892992", "1892992 2 946496", "946496 2 473248", "473248 2 236624", "236624 2 118312", "118312 2 59156", "59156 2 29578", "29578 2 14789", "14789 23 643", "643 643 1" ]

501219

3 3 55691

[ "501219 3 167073", "167073 3 55691", "55691 55691 1" ]

3819293

31 123203

[ "3819293 31 123203", "123203 123203 1" ]

3477954

2 3 449 1291

[ "3477954 2 1738977", "1738977 3 579659", "579659 449 1291", "1291 1291 1" ]

785792

2 2 2 2 2 2 2 7 877

[ "785792 2 392896", "392896 2 196448", "196448 2 98224", "98224 2 49112", "49112 2 24556", "24556 2 12278", "12278 2 6139", "6139 7 877", "877 877 1" ]

2755162

2 919 1499

[ "2755162 2 1377581", "1377581 919 1499", "1499 1499 1" ]

2867775

3 5 5 38237

[ "2867775 3 955925", "955925 5 191185", "191185 5 38237", "38237 38237 1" ]

3084341

13 237257

[ "3084341 13 237257", "237257 237257 1" ]

4183983

3 3 397 1171

[ "4183983 3 1394661", "1394661 3 464887", "464887 397 1171", "1171 1171 1" ]

1005734

2 37 13591

[ "1005734 2 502867", "502867 37 13591", "13591 13591 1" ]

2386871

23 157 661

[ "2386871 23 103777", "103777 157 661", "661 661 1" ]

1293865

5 23 11251

[ "1293865 5 258773", "258773 23 11251", "11251 11251 1" ]

1422845

5 383 743

[ "1422845 5 284569", "284569 383 743", "743 743 1" ]

1990373

7 11 25849

[ "1990373 7 284339", "284339 11 25849", "25849 25849 1" ]

3403096

2 2 2 425387

[ "3403096 2 1701548", "1701548 2 850774", "850774 2 425387", "425387 425387 1" ]

2810597

[ "2810597 2810597 1" ]