yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1883544	2 2 2 3 13 6037	[ "1883544 2 941772", "941772 2 470886", "470886 2 235443", "235443 3 78481", "78481 13 6037", "6037 6037 1" ]
977355	3 3 5 37 587	[ "977355 3 325785", "325785 3 108595", "108595 5 21719", "21719 37 587", "587 587 1" ]
3430851	3 709 1613	[ "3430851 3 1143617", "1143617 709 1613", "1613 1613 1" ]
4677441	3 23 67789	[ "4677441 3 1559147", "1559147 23 67789", "67789 67789 1" ]
95304	2 2 2 3 11 19 19	[ "95304 2 47652", "47652 2 23826", "23826 2 11913", "11913 3 3971", "3971 11 361", "361 19 19", "19 19 1" ]
4235964	2 2 3 31 59 193	[ "4235964 2 2117982", "2117982 2 1058991", "1058991 3 352997", "352997 31 11387", "11387 59 193", "193 193 1" ]
1846183	17 131 829	[ "1846183 17 108599", "108599 131 829", "829 829 1" ]
2443370	2 5 163 1499	[ "2443370 2 1221685", "1221685 5 244337", "244337 163 1499", "1499 1499 1" ]
3353349	3 41 137 199	[ "3353349 3 1117783", "1117783 41 27263", "27263 137 199", "199 199 1" ]
1276884	2 2 3 3 3 3 7 563	[ "1276884 2 638442", "638442 2 319221", "319221 3 106407", "106407 3 35469", "35469 3 11823", "11823 3 3941", "3941 7 563", "563 563 1" ]
245941	245941	[ "245941 245941 1" ]
4312073	4312073	[ "4312073 4312073 1" ]
4227935	5 31 27277	[ "4227935 5 845587", "845587 31 27277", "27277 27277 1" ]
2433400	2 2 2 5 5 23 23 23	[ "2433400 2 1216700", "1216700 2 608350", "608350 2 304175", "304175 5 60835", "60835 5 12167", "12167 23 529", "529 23 23", "23 23 1" ]
1482888	2 2 2 3 11 41 137	[ "1482888 2 741444", "741444 2 370722", "370722 2 185361", "185361 3 61787", "61787 11 5617", "5617 41 137", "137 137 1" ]
4153127	11 377557	[ "4153127 11 377557", "377557 377557 1" ]
1243289	181 6869	[ "1243289 181 6869", "6869 6869 1" ]
1982126	2 991063	[ "1982126 2 991063", "991063 991063 1" ]
2109063	3 11 79 809	[ "2109063 3 703021", "703021 11 63911", "63911 79 809", "809 809 1" ]
2066626	2 1033313	[ "2066626 2 1033313", "1033313 1033313 1" ]
2492304	2 2 2 2 3 137 379	[ "2492304 2 1246152", "1246152 2 623076", "623076 2 311538", "311538 2 155769", "155769 3 51923", "51923 137 379", "379 379 1" ]
2032426	2 11 92383	[ "2032426 2 1016213", "1016213 11 92383", "92383 92383 1" ]
2908159	19 269 569	[ "2908159 19 153061", "153061 269 569", "569 569 1" ]
388142	2 194071	[ "388142 2 194071", "194071 194071 1" ]
4153882	2 17 122173	[ "4153882 2 2076941", "2076941 17 122173", "122173 122173 1" ]
4608311	4608311	[ "4608311 4608311 1" ]
3792761	7 19 28517	[ "3792761 7 541823", "541823 19 28517", "28517 28517 1" ]
3873216	2 2 2 2 2 2 3 20173	[ "3873216 2 1936608", "1936608 2 968304", "968304 2 484152", "484152 2 242076", "242076 2 121038", "121038 2 60519", "60519 3 20173", "20173 20173 1" ]
147126	2 3 7 31 113	[ "147126 2 73563", "73563 3 24521", "24521 7 3503", "3503 31 113", "113 113 1" ]
3287771	3287771	[ "3287771 3287771 1" ]
4449840	2 2 2 2 3 5 18541	[ "4449840 2 2224920", "2224920 2 1112460", "1112460 2 556230", "556230 2 278115", "278115 3 92705", "92705 5 18541", "18541 18541 1" ]
2009670	2 3 5 13 5153	[ "2009670 2 1004835", "1004835 3 334945", "334945 5 66989", "66989 13 5153", "5153 5153 1" ]
1980013	7 41 6899	[ "1980013 7 282859", "282859 41 6899", "6899 6899 1" ]
967591	157 6163	[ "967591 157 6163", "6163 6163 1" ]
1940314	2 103 9419	[ "1940314 2 970157", "970157 103 9419", "9419 9419 1" ]
4983015	3 5 332201	[ "4983015 3 1661005", "1661005 5 332201", "332201 332201 1" ]
1983943	13 101 1511	[ "1983943 13 152611", "152611 101 1511", "1511 1511 1" ]
3325353	3 17 65203	[ "3325353 3 1108451", "1108451 17 65203", "65203 65203 1" ]
2764516	2 2 691129	[ "2764516 2 1382258", "1382258 2 691129", "691129 691129 1" ]
4743770	2 5 37 12821	[ "4743770 2 2371885", "2371885 5 474377", "474377 37 12821", "12821 12821 1" ]
2384731	67 35593	[ "2384731 67 35593", "35593 35593 1" ]
2942013	3 293 3347	[ "2942013 3 980671", "980671 293 3347", "3347 3347 1" ]
703127	703127	[ "703127 703127 1" ]
2235612	2 2 3 186301	[ "2235612 2 1117806", "1117806 2 558903", "558903 3 186301", "186301 186301 1" ]
3174783	3 661 1601	[ "3174783 3 1058261", "1058261 661 1601", "1601 1601 1" ]
3066630	2 3 5 7 17 859	[ "3066630 2 1533315", "1533315 3 511105", "511105 5 102221", "102221 7 14603", "14603 17 859", "859 859 1" ]
1254471	3 418157	[ "1254471 3 418157", "418157 418157 1" ]
3740736	2 2 2 2 2 2 3 19483	[ "3740736 2 1870368", "1870368 2 935184", "935184 2 467592", "467592 2 233796", "233796 2 116898", "116898 2 58449", "58449 3 19483", "19483 19483 1" ]
1434827	1434827	[ "1434827 1434827 1" ]
4995767	7 713681	[ "4995767 7 713681", "713681 713681 1" ]
1700806	2 850403	[ "1700806 2 850403", "850403 850403 1" ]
4957098	2 3 17 23 2113	[ "4957098 2 2478549", "2478549 3 826183", "826183 17 48599", "48599 23 2113", "2113 2113 1" ]
2799464	2 2 2 349933	[ "2799464 2 1399732", "1399732 2 699866", "699866 2 349933", "349933 349933 1" ]
318806	2 159403	[ "318806 2 159403", "159403 159403 1" ]
4327184	2 2 2 2 229 1181	[ "4327184 2 2163592", "2163592 2 1081796", "1081796 2 540898", "540898 2 270449", "270449 229 1181", "1181 1181 1" ]
4780800	2 2 2 2 2 2 2 2 3 3 5 5 83	[ "4780800 2 2390400", "2390400 2 1195200", "1195200 2 597600", "597600 2 298800", "298800 2 149400", "149400 2 74700", "74700 2 37350", "37350 2 18675", "18675 3 6225", "6225 3 2075", "2075 5 415", "415 5 83", "83 83 1" ]
4399364	2 2 1099841	[ "4399364 2 2199682", "2199682 2 1099841", "1099841 1099841 1" ]
3031001	3031001	[ "3031001 3031001 1" ]
543673	13 13 3217	[ "543673 13 41821", "41821 13 3217", "3217 3217 1" ]
3225109	349 9241	[ "3225109 349 9241", "9241 9241 1" ]
78859	11 67 107	[ "78859 11 7169", "7169 67 107", "107 107 1" ]
1761138	2 3 3 97841	[ "1761138 2 880569", "880569 3 293523", "293523 3 97841", "97841 97841 1" ]
1879862	2 939931	[ "1879862 2 939931", "939931 939931 1" ]
1056855	3 5 70457	[ "1056855 3 352285", "352285 5 70457", "70457 70457 1" ]
1414592	2 2 2 2 2 2 23 31 31	[ "1414592 2 707296", "707296 2 353648", "353648 2 176824", "176824 2 88412", "88412 2 44206", "44206 2 22103", "22103 23 961", "961 31 31", "31 31 1" ]
589867	41 14387	[ "589867 41 14387", "14387 14387 1" ]
3818774	2 373 5119	[ "3818774 2 1909387", "1909387 373 5119", "5119 5119 1" ]
987512	2 2 2 123439	[ "987512 2 493756", "493756 2 246878", "246878 2 123439", "123439 123439 1" ]
302227	302227	[ "302227 302227 1" ]
1179320	2 2 2 5 29483	[ "1179320 2 589660", "589660 2 294830", "294830 2 147415", "147415 5 29483", "29483 29483 1" ]
189170	2 5 18917	[ "189170 2 94585", "94585 5 18917", "18917 18917 1" ]
2974731	3 53 53 353	[ "2974731 3 991577", "991577 53 18709", "18709 53 353", "353 353 1" ]
1541553	3 13 29 29 47	[ "1541553 3 513851", "513851 13 39527", "39527 29 1363", "1363 29 47", "47 47 1" ]
863947	7 83 1487	[ "863947 7 123421", "123421 83 1487", "1487 1487 1" ]
3853109	13 83 3571	[ "3853109 13 296393", "296393 83 3571", "3571 3571 1" ]
1676164	2 2 7 59863	[ "1676164 2 838082", "838082 2 419041", "419041 7 59863", "59863 59863 1" ]
1942639	331 5869	[ "1942639 331 5869", "5869 5869 1" ]
4346806	2 103 21101	[ "4346806 2 2173403", "2173403 103 21101", "21101 21101 1" ]
722892	2 2 3 107 563	[ "722892 2 361446", "361446 2 180723", "180723 3 60241", "60241 107 563", "563 563 1" ]
2361628	2 2 590407	[ "2361628 2 1180814", "1180814 2 590407", "590407 590407 1" ]
472135	5 94427	[ "472135 5 94427", "94427 94427 1" ]
4714765	5 11 11 7793	[ "4714765 5 942953", "942953 11 85723", "85723 11 7793", "7793 7793 1" ]
2262853	17 133109	[ "2262853 17 133109", "133109 133109 1" ]
2850729	3 7 29 31 151	[ "2850729 3 950243", "950243 7 135749", "135749 29 4681", "4681 31 151", "151 151 1" ]
4971517	59 84263	[ "4971517 59 84263", "84263 84263 1" ]
3451957	29 119033	[ "3451957 29 119033", "119033 119033 1" ]
2306474	2 1153237	[ "2306474 2 1153237", "1153237 1153237 1" ]
2659043	2659043	[ "2659043 2659043 1" ]
4356105	3 5 13 89 251	[ "4356105 3 1452035", "1452035 5 290407", "290407 13 22339", "22339 89 251", "251 251 1" ]
2729781	3 3 3 3 67 503	[ "2729781 3 909927", "909927 3 303309", "303309 3 101103", "101103 3 33701", "33701 67 503", "503 503 1" ]
4546977	3 307 4937	[ "4546977 3 1515659", "1515659 307 4937", "4937 4937 1" ]
3817170	2 3 3 5 7 73 83	[ "3817170 2 1908585", "1908585 3 636195", "636195 3 212065", "212065 5 42413", "42413 7 6059", "6059 73 83", "83 83 1" ]
1988263	1988263	[ "1988263 1988263 1" ]
1675522	2 331 2531	[ "1675522 2 837761", "837761 331 2531", "2531 2531 1" ]
1440723	3 79 6079	[ "1440723 3 480241", "480241 79 6079", "6079 6079 1" ]
817990	2 5 81799	[ "817990 2 408995", "408995 5 81799", "81799 81799 1" ]
1780644	2 2 3 148387	[ "1780644 2 890322", "890322 2 445161", "445161 3 148387", "148387 148387 1" ]
1954801	821 2381	[ "1954801 821 2381", "2381 2381 1" ]
4478200	2 2 2 5 5 22391	[ "4478200 2 2239100", "2239100 2 1119550", "1119550 2 559775", "559775 5 111955", "111955 5 22391", "22391 22391 1" ]
2913795	3 3 5 73 887	[ "2913795 3 971265", "971265 3 323755", "323755 5 64751", "64751 73 887", "887 887 1" ]

1883544

2 2 2 3 13 6037

[ "1883544 2 941772", "941772 2 470886", "470886 2 235443", "235443 3 78481", "78481 13 6037", "6037 6037 1" ]

977355

3 3 5 37 587

[ "977355 3 325785", "325785 3 108595", "108595 5 21719", "21719 37 587", "587 587 1" ]

3430851

3 709 1613

[ "3430851 3 1143617", "1143617 709 1613", "1613 1613 1" ]

4677441

3 23 67789

[ "4677441 3 1559147", "1559147 23 67789", "67789 67789 1" ]

95304

2 2 2 3 11 19 19

[ "95304 2 47652", "47652 2 23826", "23826 2 11913", "11913 3 3971", "3971 11 361", "361 19 19", "19 19 1" ]

4235964

2 2 3 31 59 193

[ "4235964 2 2117982", "2117982 2 1058991", "1058991 3 352997", "352997 31 11387", "11387 59 193", "193 193 1" ]

1846183

17 131 829

[ "1846183 17 108599", "108599 131 829", "829 829 1" ]

2443370

2 5 163 1499

[ "2443370 2 1221685", "1221685 5 244337", "244337 163 1499", "1499 1499 1" ]

3353349

3 41 137 199

[ "3353349 3 1117783", "1117783 41 27263", "27263 137 199", "199 199 1" ]

1276884

2 2 3 3 3 3 7 563

[ "1276884 2 638442", "638442 2 319221", "319221 3 106407", "106407 3 35469", "35469 3 11823", "11823 3 3941", "3941 7 563", "563 563 1" ]

245941

[ "245941 245941 1" ]

4312073

[ "4312073 4312073 1" ]

4227935

5 31 27277

[ "4227935 5 845587", "845587 31 27277", "27277 27277 1" ]

2433400

2 2 2 5 5 23 23 23

[ "2433400 2 1216700", "1216700 2 608350", "608350 2 304175", "304175 5 60835", "60835 5 12167", "12167 23 529", "529 23 23", "23 23 1" ]

1482888

2 2 2 3 11 41 137

[ "1482888 2 741444", "741444 2 370722", "370722 2 185361", "185361 3 61787", "61787 11 5617", "5617 41 137", "137 137 1" ]

4153127

11 377557

[ "4153127 11 377557", "377557 377557 1" ]

1243289

181 6869

[ "1243289 181 6869", "6869 6869 1" ]

1982126

2 991063

[ "1982126 2 991063", "991063 991063 1" ]

2109063

3 11 79 809

[ "2109063 3 703021", "703021 11 63911", "63911 79 809", "809 809 1" ]

2066626

2 1033313

[ "2066626 2 1033313", "1033313 1033313 1" ]

2492304

2 2 2 2 3 137 379

[ "2492304 2 1246152", "1246152 2 623076", "623076 2 311538", "311538 2 155769", "155769 3 51923", "51923 137 379", "379 379 1" ]

2032426

2 11 92383

[ "2032426 2 1016213", "1016213 11 92383", "92383 92383 1" ]

2908159

19 269 569

[ "2908159 19 153061", "153061 269 569", "569 569 1" ]

388142

2 194071

[ "388142 2 194071", "194071 194071 1" ]

4153882

2 17 122173

[ "4153882 2 2076941", "2076941 17 122173", "122173 122173 1" ]

4608311

[ "4608311 4608311 1" ]

3792761

7 19 28517

[ "3792761 7 541823", "541823 19 28517", "28517 28517 1" ]

3873216

2 2 2 2 2 2 3 20173

[ "3873216 2 1936608", "1936608 2 968304", "968304 2 484152", "484152 2 242076", "242076 2 121038", "121038 2 60519", "60519 3 20173", "20173 20173 1" ]

147126

2 3 7 31 113

[ "147126 2 73563", "73563 3 24521", "24521 7 3503", "3503 31 113", "113 113 1" ]

3287771

[ "3287771 3287771 1" ]

4449840

2 2 2 2 3 5 18541

[ "4449840 2 2224920", "2224920 2 1112460", "1112460 2 556230", "556230 2 278115", "278115 3 92705", "92705 5 18541", "18541 18541 1" ]

2009670

2 3 5 13 5153

[ "2009670 2 1004835", "1004835 3 334945", "334945 5 66989", "66989 13 5153", "5153 5153 1" ]

1980013

7 41 6899

[ "1980013 7 282859", "282859 41 6899", "6899 6899 1" ]

967591

157 6163

[ "967591 157 6163", "6163 6163 1" ]

1940314

2 103 9419

[ "1940314 2 970157", "970157 103 9419", "9419 9419 1" ]

4983015

3 5 332201

[ "4983015 3 1661005", "1661005 5 332201", "332201 332201 1" ]

1983943

13 101 1511

[ "1983943 13 152611", "152611 101 1511", "1511 1511 1" ]

3325353

3 17 65203

[ "3325353 3 1108451", "1108451 17 65203", "65203 65203 1" ]

2764516

2 2 691129

[ "2764516 2 1382258", "1382258 2 691129", "691129 691129 1" ]

4743770

2 5 37 12821

[ "4743770 2 2371885", "2371885 5 474377", "474377 37 12821", "12821 12821 1" ]

2384731

67 35593

[ "2384731 67 35593", "35593 35593 1" ]

2942013

3 293 3347

[ "2942013 3 980671", "980671 293 3347", "3347 3347 1" ]

703127

[ "703127 703127 1" ]

2235612

2 2 3 186301

[ "2235612 2 1117806", "1117806 2 558903", "558903 3 186301", "186301 186301 1" ]

3174783

3 661 1601

[ "3174783 3 1058261", "1058261 661 1601", "1601 1601 1" ]

3066630

2 3 5 7 17 859

[ "3066630 2 1533315", "1533315 3 511105", "511105 5 102221", "102221 7 14603", "14603 17 859", "859 859 1" ]

1254471

3 418157

[ "1254471 3 418157", "418157 418157 1" ]

3740736

2 2 2 2 2 2 3 19483

[ "3740736 2 1870368", "1870368 2 935184", "935184 2 467592", "467592 2 233796", "233796 2 116898", "116898 2 58449", "58449 3 19483", "19483 19483 1" ]

1434827

[ "1434827 1434827 1" ]

4995767

7 713681

[ "4995767 7 713681", "713681 713681 1" ]

1700806

2 850403

[ "1700806 2 850403", "850403 850403 1" ]

4957098

2 3 17 23 2113

[ "4957098 2 2478549", "2478549 3 826183", "826183 17 48599", "48599 23 2113", "2113 2113 1" ]

2799464

2 2 2 349933

[ "2799464 2 1399732", "1399732 2 699866", "699866 2 349933", "349933 349933 1" ]

318806

2 159403

[ "318806 2 159403", "159403 159403 1" ]

4327184

2 2 2 2 229 1181

[ "4327184 2 2163592", "2163592 2 1081796", "1081796 2 540898", "540898 2 270449", "270449 229 1181", "1181 1181 1" ]

4780800

2 2 2 2 2 2 2 2 3 3 5 5 83

[ "4780800 2 2390400", "2390400 2 1195200", "1195200 2 597600", "597600 2 298800", "298800 2 149400", "149400 2 74700", "74700 2 37350", "37350 2 18675", "18675 3 6225", "6225 3 2075", "2075 5 415", "415 5 83", "83 83 1" ]

4399364

2 2 1099841

[ "4399364 2 2199682", "2199682 2 1099841", "1099841 1099841 1" ]

3031001

[ "3031001 3031001 1" ]

543673

13 13 3217

[ "543673 13 41821", "41821 13 3217", "3217 3217 1" ]

3225109

349 9241

[ "3225109 349 9241", "9241 9241 1" ]

78859

11 67 107

[ "78859 11 7169", "7169 67 107", "107 107 1" ]

1761138

2 3 3 97841

[ "1761138 2 880569", "880569 3 293523", "293523 3 97841", "97841 97841 1" ]

1879862

2 939931

[ "1879862 2 939931", "939931 939931 1" ]

1056855

3 5 70457

[ "1056855 3 352285", "352285 5 70457", "70457 70457 1" ]

1414592

2 2 2 2 2 2 23 31 31

[ "1414592 2 707296", "707296 2 353648", "353648 2 176824", "176824 2 88412", "88412 2 44206", "44206 2 22103", "22103 23 961", "961 31 31", "31 31 1" ]

589867

41 14387

[ "589867 41 14387", "14387 14387 1" ]

3818774

2 373 5119

[ "3818774 2 1909387", "1909387 373 5119", "5119 5119 1" ]

987512

2 2 2 123439

[ "987512 2 493756", "493756 2 246878", "246878 2 123439", "123439 123439 1" ]

302227

[ "302227 302227 1" ]

1179320

2 2 2 5 29483

[ "1179320 2 589660", "589660 2 294830", "294830 2 147415", "147415 5 29483", "29483 29483 1" ]

189170

2 5 18917

[ "189170 2 94585", "94585 5 18917", "18917 18917 1" ]

2974731

3 53 53 353

[ "2974731 3 991577", "991577 53 18709", "18709 53 353", "353 353 1" ]

1541553

3 13 29 29 47

[ "1541553 3 513851", "513851 13 39527", "39527 29 1363", "1363 29 47", "47 47 1" ]

863947

7 83 1487

[ "863947 7 123421", "123421 83 1487", "1487 1487 1" ]

3853109

13 83 3571

[ "3853109 13 296393", "296393 83 3571", "3571 3571 1" ]

1676164

2 2 7 59863

[ "1676164 2 838082", "838082 2 419041", "419041 7 59863", "59863 59863 1" ]

1942639

331 5869

[ "1942639 331 5869", "5869 5869 1" ]

4346806

2 103 21101

[ "4346806 2 2173403", "2173403 103 21101", "21101 21101 1" ]

722892

2 2 3 107 563

[ "722892 2 361446", "361446 2 180723", "180723 3 60241", "60241 107 563", "563 563 1" ]

2361628

2 2 590407

[ "2361628 2 1180814", "1180814 2 590407", "590407 590407 1" ]

472135

5 94427

[ "472135 5 94427", "94427 94427 1" ]

4714765

5 11 11 7793

[ "4714765 5 942953", "942953 11 85723", "85723 11 7793", "7793 7793 1" ]

2262853

17 133109

[ "2262853 17 133109", "133109 133109 1" ]

2850729

3 7 29 31 151

[ "2850729 3 950243", "950243 7 135749", "135749 29 4681", "4681 31 151", "151 151 1" ]

4971517

59 84263

[ "4971517 59 84263", "84263 84263 1" ]

3451957

29 119033

[ "3451957 29 119033", "119033 119033 1" ]

2306474

2 1153237

[ "2306474 2 1153237", "1153237 1153237 1" ]

2659043

[ "2659043 2659043 1" ]

4356105

3 5 13 89 251

[ "4356105 3 1452035", "1452035 5 290407", "290407 13 22339", "22339 89 251", "251 251 1" ]

2729781

3 3 3 3 67 503

[ "2729781 3 909927", "909927 3 303309", "303309 3 101103", "101103 3 33701", "33701 67 503", "503 503 1" ]

4546977

3 307 4937

[ "4546977 3 1515659", "1515659 307 4937", "4937 4937 1" ]

3817170

2 3 3 5 7 73 83

[ "3817170 2 1908585", "1908585 3 636195", "636195 3 212065", "212065 5 42413", "42413 7 6059", "6059 73 83", "83 83 1" ]

1988263

[ "1988263 1988263 1" ]

1675522

2 331 2531

[ "1675522 2 837761", "837761 331 2531", "2531 2531 1" ]

1440723

3 79 6079

[ "1440723 3 480241", "480241 79 6079", "6079 6079 1" ]

817990

2 5 81799

[ "817990 2 408995", "408995 5 81799", "81799 81799 1" ]

1780644

2 2 3 148387

[ "1780644 2 890322", "890322 2 445161", "445161 3 148387", "148387 148387 1" ]

1954801

821 2381

[ "1954801 821 2381", "2381 2381 1" ]

4478200

2 2 2 5 5 22391

[ "4478200 2 2239100", "2239100 2 1119550", "1119550 2 559775", "559775 5 111955", "111955 5 22391", "22391 22391 1" ]

2913795

3 3 5 73 887

[ "2913795 3 971265", "971265 3 323755", "323755 5 64751", "64751 73 887", "887 887 1" ]