yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1941369	3 653 991	[ "1941369 3 647123", "647123 653 991", "991 991 1" ]
636538	2 7 19 2393	[ "636538 2 318269", "318269 7 45467", "45467 19 2393", "2393 2393 1" ]
3803420	2 2 5 19 10009	[ "3803420 2 1901710", "1901710 2 950855", "950855 5 190171", "190171 19 10009", "10009 10009 1" ]
4434422	2 2217211	[ "4434422 2 2217211", "2217211 2217211 1" ]
3854037	3 11 116789	[ "3854037 3 1284679", "1284679 11 116789", "116789 116789 1" ]
1159613	7 13 12743	[ "1159613 7 165659", "165659 13 12743", "12743 12743 1" ]
3075890	2 5 307589	[ "3075890 2 1537945", "1537945 5 307589", "307589 307589 1" ]
4232739	3 7 53 3803	[ "4232739 3 1410913", "1410913 7 201559", "201559 53 3803", "3803 3803 1" ]
2343731	13 180287	[ "2343731 13 180287", "180287 180287 1" ]
128749	128749	[ "128749 128749 1" ]
207238	2 103619	[ "207238 2 103619", "103619 103619 1" ]
432555	3 5 28837	[ "432555 3 144185", "144185 5 28837", "28837 28837 1" ]
2431289	7 17 20431	[ "2431289 7 347327", "347327 17 20431", "20431 20431 1" ]
3891047	199 19553	[ "3891047 199 19553", "19553 19553 1" ]
2012073	3 7 95813	[ "2012073 3 670691", "670691 7 95813", "95813 95813 1" ]
4464088	2 2 2 19 43 683	[ "4464088 2 2232044", "2232044 2 1116022", "1116022 2 558011", "558011 19 29369", "29369 43 683", "683 683 1" ]
2295616	2 2 2 2 2 2 35869	[ "2295616 2 1147808", "1147808 2 573904", "573904 2 286952", "286952 2 143476", "143476 2 71738", "71738 2 35869", "35869 35869 1" ]
3098912	2 2 2 2 2 113 857	[ "3098912 2 1549456", "1549456 2 774728", "774728 2 387364", "387364 2 193682", "193682 2 96841", "96841 113 857", "857 857 1" ]
4833485	5 449 2153	[ "4833485 5 966697", "966697 449 2153", "2153 2153 1" ]
451903	451903	[ "451903 451903 1" ]
4557921	3 17 89371	[ "4557921 3 1519307", "1519307 17 89371", "89371 89371 1" ]
4512607	11 277 1481	[ "4512607 11 410237", "410237 277 1481", "1481 1481 1" ]
3685711	137 26903	[ "3685711 137 26903", "26903 26903 1" ]
4977283	53 93911	[ "4977283 53 93911", "93911 93911 1" ]
3164015	5 31 137 149	[ "3164015 5 632803", "632803 31 20413", "20413 137 149", "149 149 1" ]
2229136	2 2 2 2 7 13 1531	[ "2229136 2 1114568", "1114568 2 557284", "557284 2 278642", "278642 2 139321", "139321 7 19903", "19903 13 1531", "1531 1531 1" ]
918881	97 9473	[ "918881 97 9473", "9473 9473 1" ]
448329	3 7 37 577	[ "448329 3 149443", "149443 7 21349", "21349 37 577", "577 577 1" ]
1907919	3 3 13 23 709	[ "1907919 3 635973", "635973 3 211991", "211991 13 16307", "16307 23 709", "709 709 1" ]
781555	5 67 2333	[ "781555 5 156311", "156311 67 2333", "2333 2333 1" ]
2736249	3 912083	[ "2736249 3 912083", "912083 912083 1" ]
1204763	7 7 23 1069	[ "1204763 7 172109", "172109 7 24587", "24587 23 1069", "1069 1069 1" ]
671108	2 2 167777	[ "671108 2 335554", "335554 2 167777", "167777 167777 1" ]
2754633	3 7 7 7 2677	[ "2754633 3 918211", "918211 7 131173", "131173 7 18739", "18739 7 2677", "2677 2677 1" ]
1287124	2 2 151 2131	[ "1287124 2 643562", "643562 2 321781", "321781 151 2131", "2131 2131 1" ]
1572609	3 524203	[ "1572609 3 524203", "524203 524203 1" ]
4857879	3 13 124561	[ "4857879 3 1619293", "1619293 13 124561", "124561 124561 1" ]
2163049	7 309007	[ "2163049 7 309007", "309007 309007 1" ]
4769321	101 47221	[ "4769321 101 47221", "47221 47221 1" ]
4396259	7 628037	[ "4396259 7 628037", "628037 628037 1" ]
169597	181 937	[ "169597 181 937", "937 937 1" ]
170907	3 11 5179	[ "170907 3 56969", "56969 11 5179", "5179 5179 1" ]
4606279	23 200273	[ "4606279 23 200273", "200273 200273 1" ]
2200568	2 2 2 43 6397	[ "2200568 2 1100284", "1100284 2 550142", "550142 2 275071", "275071 43 6397", "6397 6397 1" ]
1226330	2 5 7 17519	[ "1226330 2 613165", "613165 5 122633", "122633 7 17519", "17519 17519 1" ]
3023827	241 12547	[ "3023827 241 12547", "12547 12547 1" ]
2575781	13 347 571	[ "2575781 13 198137", "198137 347 571", "571 571 1" ]
4344835	5 11 197 401	[ "4344835 5 868967", "868967 11 78997", "78997 197 401", "401 401 1" ]
3890285	5 7 41 2711	[ "3890285 5 778057", "778057 7 111151", "111151 41 2711", "2711 2711 1" ]
4123516	2 2 599 1721	[ "4123516 2 2061758", "2061758 2 1030879", "1030879 599 1721", "1721 1721 1" ]
536063	11 48733	[ "536063 11 48733", "48733 48733 1" ]
1871885	5 317 1181	[ "1871885 5 374377", "374377 317 1181", "1181 1181 1" ]
1500529	1500529	[ "1500529 1500529 1" ]
35885	5 7177	[ "35885 5 7177", "7177 7177 1" ]
2668243	2668243	[ "2668243 2668243 1" ]
1331615	5 19 107 131	[ "1331615 5 266323", "266323 19 14017", "14017 107 131", "131 131 1" ]
4489615	5 13 17 17 239	[ "4489615 5 897923", "897923 13 69071", "69071 17 4063", "4063 17 239", "239 239 1" ]
4769393	97 49169	[ "4769393 97 49169", "49169 49169 1" ]
1392826	2 696413	[ "1392826 2 696413", "696413 696413 1" ]
809830	2 5 7 23 503	[ "809830 2 404915", "404915 5 80983", "80983 7 11569", "11569 23 503", "503 503 1" ]
4546982	2 11 41 71 71	[ "4546982 2 2273491", "2273491 11 206681", "206681 41 5041", "5041 71 71", "71 71 1" ]
1475045	5 11 13 2063	[ "1475045 5 295009", "295009 11 26819", "26819 13 2063", "2063 2063 1" ]
4844063	7 692009	[ "4844063 7 692009", "692009 692009 1" ]
4891911	3 19 19 4517	[ "4891911 3 1630637", "1630637 19 85823", "85823 19 4517", "4517 4517 1" ]
480882	2 3 80147	[ "480882 2 240441", "240441 3 80147", "80147 80147 1" ]
3600878	2 487 3697	[ "3600878 2 1800439", "1800439 487 3697", "3697 3697 1" ]
4862	2 11 13 17	[ "4862 2 2431", "2431 11 221", "221 13 17", "17 17 1" ]
1291666	2 645833	[ "1291666 2 645833", "645833 645833 1" ]
4956769	1063 4663	[ "4956769 1063 4663", "4663 4663 1" ]
4643516	2 2 17 23 2969	[ "4643516 2 2321758", "2321758 2 1160879", "1160879 17 68287", "68287 23 2969", "2969 2969 1" ]
3283469	7 67 7001	[ "3283469 7 469067", "469067 67 7001", "7001 7001 1" ]
3135562	2 139 11279	[ "3135562 2 1567781", "1567781 139 11279", "11279 11279 1" ]
3033071	31 97841	[ "3033071 31 97841", "97841 97841 1" ]
1713565	5 7 173 283	[ "1713565 5 342713", "342713 7 48959", "48959 173 283", "283 283 1" ]
3857604	2 2 3 321467	[ "3857604 2 1928802", "1928802 2 964401", "964401 3 321467", "321467 321467 1" ]
1742502	2 3 83 3499	[ "1742502 2 871251", "871251 3 290417", "290417 83 3499", "3499 3499 1" ]
2651420	2 2 5 37 3583	[ "2651420 2 1325710", "1325710 2 662855", "662855 5 132571", "132571 37 3583", "3583 3583 1" ]
2371929	3 7 179 631	[ "2371929 3 790643", "790643 7 112949", "112949 179 631", "631 631 1" ]
633293	673 941	[ "633293 673 941", "941 941 1" ]
4162832	2 2 2 2 53 4909	[ "4162832 2 2081416", "2081416 2 1040708", "1040708 2 520354", "520354 2 260177", "260177 53 4909", "4909 4909 1" ]
283737	3 271 349	[ "283737 3 94579", "94579 271 349", "349 349 1" ]
4669384	2 2 2 583673	[ "4669384 2 2334692", "2334692 2 1167346", "1167346 2 583673", "583673 583673 1" ]
3725593	251 14843	[ "3725593 251 14843", "14843 14843 1" ]
358512	2 2 2 2 3 7 11 97	[ "358512 2 179256", "179256 2 89628", "89628 2 44814", "44814 2 22407", "22407 3 7469", "7469 7 1067", "1067 11 97", "97 97 1" ]
542153	542153	[ "542153 542153 1" ]
632576	2 2 2 2 2 2 2 2 7 353	[ "632576 2 316288", "316288 2 158144", "158144 2 79072", "79072 2 39536", "39536 2 19768", "19768 2 9884", "9884 2 4942", "4942 2 2471", "2471 7 353", "353 353 1" ]
4643448	2 2 2 3 17 19 599	[ "4643448 2 2321724", "2321724 2 1160862", "1160862 2 580431", "580431 3 193477", "193477 17 11381", "11381 19 599", "599 599 1" ]
786359	7 112337	[ "786359 7 112337", "112337 112337 1" ]
3516330	2 3 5 19 31 199	[ "3516330 2 1758165", "1758165 3 586055", "586055 5 117211", "117211 19 6169", "6169 31 199", "199 199 1" ]
2804402	2 1402201	[ "2804402 2 1402201", "1402201 1402201 1" ]
2148259	97 22147	[ "2148259 97 22147", "22147 22147 1" ]
3873908	2 2 347 2791	[ "3873908 2 1936954", "1936954 2 968477", "968477 347 2791", "2791 2791 1" ]
4118919	3 7 196139	[ "4118919 3 1372973", "1372973 7 196139", "196139 196139 1" ]
2553062	2 647 1973	[ "2553062 2 1276531", "1276531 647 1973", "1973 1973 1" ]
2244792	2 2 2 3 11 11 773	[ "2244792 2 1122396", "1122396 2 561198", "561198 2 280599", "280599 3 93533", "93533 11 8503", "8503 11 773", "773 773 1" ]
431658	2 3 3 23981	[ "431658 2 215829", "215829 3 71943", "71943 3 23981", "23981 23981 1" ]
1508576	2 2 2 2 2 47143	[ "1508576 2 754288", "754288 2 377144", "377144 2 188572", "188572 2 94286", "94286 2 47143", "47143 47143 1" ]
4470339	3 19 78427	[ "4470339 3 1490113", "1490113 19 78427", "78427 78427 1" ]
2068480	2 2 2 2 2 2 2 2 2 2 2 2 5 101	[ "2068480 2 1034240", "1034240 2 517120", "517120 2 258560", "258560 2 129280", "129280 2 64640", "64640 2 32320", "32320 2 16160", "16160 2 8080", "8080 2 4040", "4040 2 2020", "2020 2 1010", "1010 2 505", "505 5 101", "101 101 1" ]
1147738	2 17 33757	[ "1147738 2 573869", "573869 17 33757", "33757 33757 1" ]

1941369

3 653 991

[ "1941369 3 647123", "647123 653 991", "991 991 1" ]

636538

2 7 19 2393

[ "636538 2 318269", "318269 7 45467", "45467 19 2393", "2393 2393 1" ]

3803420

2 2 5 19 10009

[ "3803420 2 1901710", "1901710 2 950855", "950855 5 190171", "190171 19 10009", "10009 10009 1" ]

4434422

2 2217211

[ "4434422 2 2217211", "2217211 2217211 1" ]

3854037

3 11 116789

[ "3854037 3 1284679", "1284679 11 116789", "116789 116789 1" ]

1159613

7 13 12743

[ "1159613 7 165659", "165659 13 12743", "12743 12743 1" ]

3075890

2 5 307589

[ "3075890 2 1537945", "1537945 5 307589", "307589 307589 1" ]

4232739

3 7 53 3803

[ "4232739 3 1410913", "1410913 7 201559", "201559 53 3803", "3803 3803 1" ]

2343731

13 180287

[ "2343731 13 180287", "180287 180287 1" ]

128749

[ "128749 128749 1" ]

207238

2 103619

[ "207238 2 103619", "103619 103619 1" ]

432555

3 5 28837

[ "432555 3 144185", "144185 5 28837", "28837 28837 1" ]

2431289

7 17 20431

[ "2431289 7 347327", "347327 17 20431", "20431 20431 1" ]

3891047

199 19553

[ "3891047 199 19553", "19553 19553 1" ]

2012073

3 7 95813

[ "2012073 3 670691", "670691 7 95813", "95813 95813 1" ]

4464088

2 2 2 19 43 683

[ "4464088 2 2232044", "2232044 2 1116022", "1116022 2 558011", "558011 19 29369", "29369 43 683", "683 683 1" ]

2295616

2 2 2 2 2 2 35869

[ "2295616 2 1147808", "1147808 2 573904", "573904 2 286952", "286952 2 143476", "143476 2 71738", "71738 2 35869", "35869 35869 1" ]

3098912

2 2 2 2 2 113 857

[ "3098912 2 1549456", "1549456 2 774728", "774728 2 387364", "387364 2 193682", "193682 2 96841", "96841 113 857", "857 857 1" ]

4833485

5 449 2153

[ "4833485 5 966697", "966697 449 2153", "2153 2153 1" ]

451903

[ "451903 451903 1" ]

4557921

3 17 89371

[ "4557921 3 1519307", "1519307 17 89371", "89371 89371 1" ]

4512607

11 277 1481

[ "4512607 11 410237", "410237 277 1481", "1481 1481 1" ]

3685711

137 26903

[ "3685711 137 26903", "26903 26903 1" ]

4977283

53 93911

[ "4977283 53 93911", "93911 93911 1" ]

3164015

5 31 137 149

[ "3164015 5 632803", "632803 31 20413", "20413 137 149", "149 149 1" ]

2229136

2 2 2 2 7 13 1531

[ "2229136 2 1114568", "1114568 2 557284", "557284 2 278642", "278642 2 139321", "139321 7 19903", "19903 13 1531", "1531 1531 1" ]

918881

97 9473

[ "918881 97 9473", "9473 9473 1" ]

448329

3 7 37 577

[ "448329 3 149443", "149443 7 21349", "21349 37 577", "577 577 1" ]

1907919

3 3 13 23 709

[ "1907919 3 635973", "635973 3 211991", "211991 13 16307", "16307 23 709", "709 709 1" ]

781555

5 67 2333

[ "781555 5 156311", "156311 67 2333", "2333 2333 1" ]

2736249

3 912083

[ "2736249 3 912083", "912083 912083 1" ]

1204763

7 7 23 1069

[ "1204763 7 172109", "172109 7 24587", "24587 23 1069", "1069 1069 1" ]

671108

2 2 167777

[ "671108 2 335554", "335554 2 167777", "167777 167777 1" ]

2754633

3 7 7 7 2677

[ "2754633 3 918211", "918211 7 131173", "131173 7 18739", "18739 7 2677", "2677 2677 1" ]

1287124

2 2 151 2131

[ "1287124 2 643562", "643562 2 321781", "321781 151 2131", "2131 2131 1" ]

1572609

3 524203

[ "1572609 3 524203", "524203 524203 1" ]

4857879

3 13 124561

[ "4857879 3 1619293", "1619293 13 124561", "124561 124561 1" ]

2163049

7 309007

[ "2163049 7 309007", "309007 309007 1" ]

4769321

101 47221

[ "4769321 101 47221", "47221 47221 1" ]

4396259

7 628037

[ "4396259 7 628037", "628037 628037 1" ]

169597

181 937

[ "169597 181 937", "937 937 1" ]

170907

3 11 5179

[ "170907 3 56969", "56969 11 5179", "5179 5179 1" ]

4606279

23 200273

[ "4606279 23 200273", "200273 200273 1" ]

2200568

2 2 2 43 6397

[ "2200568 2 1100284", "1100284 2 550142", "550142 2 275071", "275071 43 6397", "6397 6397 1" ]

1226330

2 5 7 17519

[ "1226330 2 613165", "613165 5 122633", "122633 7 17519", "17519 17519 1" ]

3023827

241 12547

[ "3023827 241 12547", "12547 12547 1" ]

2575781

13 347 571

[ "2575781 13 198137", "198137 347 571", "571 571 1" ]

4344835

5 11 197 401

[ "4344835 5 868967", "868967 11 78997", "78997 197 401", "401 401 1" ]

3890285

5 7 41 2711

[ "3890285 5 778057", "778057 7 111151", "111151 41 2711", "2711 2711 1" ]

4123516

2 2 599 1721

[ "4123516 2 2061758", "2061758 2 1030879", "1030879 599 1721", "1721 1721 1" ]

536063

11 48733

[ "536063 11 48733", "48733 48733 1" ]

1871885

5 317 1181

[ "1871885 5 374377", "374377 317 1181", "1181 1181 1" ]

1500529

[ "1500529 1500529 1" ]

35885

5 7177

[ "35885 5 7177", "7177 7177 1" ]

2668243

[ "2668243 2668243 1" ]

1331615

5 19 107 131

[ "1331615 5 266323", "266323 19 14017", "14017 107 131", "131 131 1" ]

4489615

5 13 17 17 239

[ "4489615 5 897923", "897923 13 69071", "69071 17 4063", "4063 17 239", "239 239 1" ]

4769393

97 49169

[ "4769393 97 49169", "49169 49169 1" ]

1392826

2 696413

[ "1392826 2 696413", "696413 696413 1" ]

809830

2 5 7 23 503

[ "809830 2 404915", "404915 5 80983", "80983 7 11569", "11569 23 503", "503 503 1" ]

4546982

2 11 41 71 71

[ "4546982 2 2273491", "2273491 11 206681", "206681 41 5041", "5041 71 71", "71 71 1" ]

1475045

5 11 13 2063

[ "1475045 5 295009", "295009 11 26819", "26819 13 2063", "2063 2063 1" ]

4844063

7 692009

[ "4844063 7 692009", "692009 692009 1" ]

4891911

3 19 19 4517

[ "4891911 3 1630637", "1630637 19 85823", "85823 19 4517", "4517 4517 1" ]

480882

2 3 80147

[ "480882 2 240441", "240441 3 80147", "80147 80147 1" ]

3600878

2 487 3697

[ "3600878 2 1800439", "1800439 487 3697", "3697 3697 1" ]

4862

2 11 13 17

[ "4862 2 2431", "2431 11 221", "221 13 17", "17 17 1" ]

1291666

2 645833

[ "1291666 2 645833", "645833 645833 1" ]

4956769

1063 4663

[ "4956769 1063 4663", "4663 4663 1" ]

4643516

2 2 17 23 2969

[ "4643516 2 2321758", "2321758 2 1160879", "1160879 17 68287", "68287 23 2969", "2969 2969 1" ]

3283469

7 67 7001

[ "3283469 7 469067", "469067 67 7001", "7001 7001 1" ]

3135562

2 139 11279

[ "3135562 2 1567781", "1567781 139 11279", "11279 11279 1" ]

3033071

31 97841

[ "3033071 31 97841", "97841 97841 1" ]

1713565

5 7 173 283

[ "1713565 5 342713", "342713 7 48959", "48959 173 283", "283 283 1" ]

3857604

2 2 3 321467

[ "3857604 2 1928802", "1928802 2 964401", "964401 3 321467", "321467 321467 1" ]

1742502

2 3 83 3499

[ "1742502 2 871251", "871251 3 290417", "290417 83 3499", "3499 3499 1" ]

2651420

2 2 5 37 3583

[ "2651420 2 1325710", "1325710 2 662855", "662855 5 132571", "132571 37 3583", "3583 3583 1" ]

2371929

3 7 179 631

[ "2371929 3 790643", "790643 7 112949", "112949 179 631", "631 631 1" ]

633293

673 941

[ "633293 673 941", "941 941 1" ]

4162832

2 2 2 2 53 4909

[ "4162832 2 2081416", "2081416 2 1040708", "1040708 2 520354", "520354 2 260177", "260177 53 4909", "4909 4909 1" ]

283737

3 271 349

[ "283737 3 94579", "94579 271 349", "349 349 1" ]

4669384

2 2 2 583673

[ "4669384 2 2334692", "2334692 2 1167346", "1167346 2 583673", "583673 583673 1" ]

3725593

251 14843

[ "3725593 251 14843", "14843 14843 1" ]

358512

2 2 2 2 3 7 11 97

[ "358512 2 179256", "179256 2 89628", "89628 2 44814", "44814 2 22407", "22407 3 7469", "7469 7 1067", "1067 11 97", "97 97 1" ]

542153

[ "542153 542153 1" ]

632576

2 2 2 2 2 2 2 2 7 353

[ "632576 2 316288", "316288 2 158144", "158144 2 79072", "79072 2 39536", "39536 2 19768", "19768 2 9884", "9884 2 4942", "4942 2 2471", "2471 7 353", "353 353 1" ]

4643448

2 2 2 3 17 19 599

[ "4643448 2 2321724", "2321724 2 1160862", "1160862 2 580431", "580431 3 193477", "193477 17 11381", "11381 19 599", "599 599 1" ]

786359

7 112337

[ "786359 7 112337", "112337 112337 1" ]

3516330

2 3 5 19 31 199

[ "3516330 2 1758165", "1758165 3 586055", "586055 5 117211", "117211 19 6169", "6169 31 199", "199 199 1" ]

2804402

2 1402201

[ "2804402 2 1402201", "1402201 1402201 1" ]

2148259

97 22147

[ "2148259 97 22147", "22147 22147 1" ]

3873908

2 2 347 2791

[ "3873908 2 1936954", "1936954 2 968477", "968477 347 2791", "2791 2791 1" ]

4118919

3 7 196139

[ "4118919 3 1372973", "1372973 7 196139", "196139 196139 1" ]

2553062

2 647 1973

[ "2553062 2 1276531", "1276531 647 1973", "1973 1973 1" ]

2244792

2 2 2 3 11 11 773

[ "2244792 2 1122396", "1122396 2 561198", "561198 2 280599", "280599 3 93533", "93533 11 8503", "8503 11 773", "773 773 1" ]

431658

2 3 3 23981

[ "431658 2 215829", "215829 3 71943", "71943 3 23981", "23981 23981 1" ]

1508576

2 2 2 2 2 47143

[ "1508576 2 754288", "754288 2 377144", "377144 2 188572", "188572 2 94286", "94286 2 47143", "47143 47143 1" ]

4470339

3 19 78427

[ "4470339 3 1490113", "1490113 19 78427", "78427 78427 1" ]

2068480

2 2 2 2 2 2 2 2 2 2 2 2 5 101

[ "2068480 2 1034240", "1034240 2 517120", "517120 2 258560", "258560 2 129280", "129280 2 64640", "64640 2 32320", "32320 2 16160", "16160 2 8080", "8080 2 4040", "4040 2 2020", "2020 2 1010", "1010 2 505", "505 5 101", "101 101 1" ]

1147738

2 17 33757

[ "1147738 2 573869", "573869 17 33757", "33757 33757 1" ]