yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
4479276	2 2 3 373273	[ "4479276 2 2239638", "2239638 2 1119819", "1119819 3 373273", "373273 373273 1" ]
1717222	2 13 66047	[ "1717222 2 858611", "858611 13 66047", "66047 66047 1" ]
4672099	4672099	[ "4672099 4672099 1" ]
2600974	2 1300487	[ "2600974 2 1300487", "1300487 1300487 1" ]
1904873	53 127 283	[ "1904873 53 35941", "35941 127 283", "283 283 1" ]
3436096	2 2 2 2 2 2 53 1013	[ "3436096 2 1718048", "1718048 2 859024", "859024 2 429512", "429512 2 214756", "214756 2 107378", "107378 2 53689", "53689 53 1013", "1013 1013 1" ]
3520414	2 151 11657	[ "3520414 2 1760207", "1760207 151 11657", "11657 11657 1" ]
3857819	7 7 131 601	[ "3857819 7 551117", "551117 7 78731", "78731 131 601", "601 601 1" ]
4343962	2 7 310283	[ "4343962 2 2171981", "2171981 7 310283", "310283 310283 1" ]
2916449	31 94079	[ "2916449 31 94079", "94079 94079 1" ]
2791875	3 5 5 5 5 1489	[ "2791875 3 930625", "930625 5 186125", "186125 5 37225", "37225 5 7445", "7445 5 1489", "1489 1489 1" ]
4703599	31 151729	[ "4703599 31 151729", "151729 151729 1" ]
3517082	2 1758541	[ "3517082 2 1758541", "1758541 1758541 1" ]
1680171	3 283 1979	[ "1680171 3 560057", "560057 283 1979", "1979 1979 1" ]
62187	3 19 1091	[ "62187 3 20729", "20729 19 1091", "1091 1091 1" ]
3809381	3809381	[ "3809381 3809381 1" ]
890429	890429	[ "890429 890429 1" ]
4686526	2 13 17 23 461	[ "4686526 2 2343263", "2343263 13 180251", "180251 17 10603", "10603 23 461", "461 461 1" ]
278485	5 55697	[ "278485 5 55697", "55697 55697 1" ]
1555318	2 353 2203	[ "1555318 2 777659", "777659 353 2203", "2203 2203 1" ]
4830509	349 13841	[ "4830509 349 13841", "13841 13841 1" ]
2818611	3 3 3 104393	[ "2818611 3 939537", "939537 3 313179", "313179 3 104393", "104393 104393 1" ]
457663	59 7757	[ "457663 59 7757", "7757 7757 1" ]
2089484	2 2 522371	[ "2089484 2 1044742", "1044742 2 522371", "522371 522371 1" ]
3998059	13 307543	[ "3998059 13 307543", "307543 307543 1" ]
312950	2 5 5 11 569	[ "312950 2 156475", "156475 5 31295", "31295 5 6259", "6259 11 569", "569 569 1" ]
1393741	53 26297	[ "1393741 53 26297", "26297 26297 1" ]
2886411	3 11 47 1861	[ "2886411 3 962137", "962137 11 87467", "87467 47 1861", "1861 1861 1" ]
806120	2 2 2 5 7 2879	[ "806120 2 403060", "403060 2 201530", "201530 2 100765", "100765 5 20153", "20153 7 2879", "2879 2879 1" ]
467510	2 5 46751	[ "467510 2 233755", "233755 5 46751", "46751 46751 1" ]
4527035	5 19 47653	[ "4527035 5 905407", "905407 19 47653", "47653 47653 1" ]
2672752	2 2 2 2 167047	[ "2672752 2 1336376", "1336376 2 668188", "668188 2 334094", "334094 2 167047", "167047 167047 1" ]
1322401	97 13633	[ "1322401 97 13633", "13633 13633 1" ]
3009506	2 37 67 607	[ "3009506 2 1504753", "1504753 37 40669", "40669 67 607", "607 607 1" ]
4746163	4746163	[ "4746163 4746163 1" ]
4457797	37 211 571	[ "4457797 37 120481", "120481 211 571", "571 571 1" ]
3248192	2 2 2 2 2 2 50753	[ "3248192 2 1624096", "1624096 2 812048", "812048 2 406024", "406024 2 203012", "203012 2 101506", "101506 2 50753", "50753 50753 1" ]
200875	5 5 5 1607	[ "200875 5 40175", "40175 5 8035", "8035 5 1607", "1607 1607 1" ]
470053	31 59 257	[ "470053 31 15163", "15163 59 257", "257 257 1" ]
1588062	2 3 7 37811	[ "1588062 2 794031", "794031 3 264677", "264677 7 37811", "37811 37811 1" ]
2947514	2 197 7481	[ "2947514 2 1473757", "1473757 197 7481", "7481 7481 1" ]
315328	2 2 2 2 2 2 13 379	[ "315328 2 157664", "157664 2 78832", "78832 2 39416", "39416 2 19708", "19708 2 9854", "9854 2 4927", "4927 13 379", "379 379 1" ]
2876934	2 3 479489	[ "2876934 2 1438467", "1438467 3 479489", "479489 479489 1" ]
2283833	2283833	[ "2283833 2283833 1" ]
521881	521881	[ "521881 521881 1" ]
1985838	2 3 17 19469	[ "1985838 2 992919", "992919 3 330973", "330973 17 19469", "19469 19469 1" ]
535206	2 3 7 12743	[ "535206 2 267603", "267603 3 89201", "89201 7 12743", "12743 12743 1" ]
3760188	2 2 3 47 59 113	[ "3760188 2 1880094", "1880094 2 940047", "940047 3 313349", "313349 47 6667", "6667 59 113", "113 113 1" ]
1370588	2 2 342647	[ "1370588 2 685294", "685294 2 342647", "342647 342647 1" ]
4706792	2 2 2 31 18979	[ "4706792 2 2353396", "2353396 2 1176698", "1176698 2 588349", "588349 31 18979", "18979 18979 1" ]
131297	131297	[ "131297 131297 1" ]
1346567	1346567	[ "1346567 1346567 1" ]
1824572	2 2 349 1307	[ "1824572 2 912286", "912286 2 456143", "456143 349 1307", "1307 1307 1" ]
467049	3 11 14153	[ "467049 3 155683", "155683 11 14153", "14153 14153 1" ]
2222534	2 103 10789	[ "2222534 2 1111267", "1111267 103 10789", "10789 10789 1" ]
4403812	2 2 7 157279	[ "4403812 2 2201906", "2201906 2 1100953", "1100953 7 157279", "157279 157279 1" ]
4492283	67 67049	[ "4492283 67 67049", "67049 67049 1" ]
1921565	5 19 113 179	[ "1921565 5 384313", "384313 19 20227", "20227 113 179", "179 179 1" ]
2384825	5 5 95393	[ "2384825 5 476965", "476965 5 95393", "95393 95393 1" ]
1635332	2 2 17 24049	[ "1635332 2 817666", "817666 2 408833", "408833 17 24049", "24049 24049 1" ]
4317140	2 2 5 215857	[ "4317140 2 2158570", "2158570 2 1079285", "1079285 5 215857", "215857 215857 1" ]
4535120	2 2 2 2 5 83 683	[ "4535120 2 2267560", "2267560 2 1133780", "1133780 2 566890", "566890 2 283445", "283445 5 56689", "56689 83 683", "683 683 1" ]
608844	2 2 3 113 449	[ "608844 2 304422", "304422 2 152211", "152211 3 50737", "50737 113 449", "449 449 1" ]
4443574	2 67 33161	[ "4443574 2 2221787", "2221787 67 33161", "33161 33161 1" ]
3352967	3352967	[ "3352967 3352967 1" ]
662242	2 7 47303	[ "662242 2 331121", "331121 7 47303", "47303 47303 1" ]
3735576	2 2 2 3 3 13 13 307	[ "3735576 2 1867788", "1867788 2 933894", "933894 2 466947", "466947 3 155649", "155649 3 51883", "51883 13 3991", "3991 13 307", "307 307 1" ]
115031	7 16433	[ "115031 7 16433", "16433 16433 1" ]
2742129	3 3 13 23 1019	[ "2742129 3 914043", "914043 3 304681", "304681 13 23437", "23437 23 1019", "1019 1019 1" ]
1898372	2 2 7 151 449	[ "1898372 2 949186", "949186 2 474593", "474593 7 67799", "67799 151 449", "449 449 1" ]
2512973	131 19183	[ "2512973 131 19183", "19183 19183 1" ]
4052163	3 23 58727	[ "4052163 3 1350721", "1350721 23 58727", "58727 58727 1" ]
3820413	3 1273471	[ "3820413 3 1273471", "1273471 1273471 1" ]
626076	2 2 3 3 3 11 17 31	[ "626076 2 313038", "313038 2 156519", "156519 3 52173", "52173 3 17391", "17391 3 5797", "5797 11 527", "527 17 31", "31 31 1" ]
831104	2 2 2 2 2 2 2 43 151	[ "831104 2 415552", "415552 2 207776", "207776 2 103888", "103888 2 51944", "51944 2 25972", "25972 2 12986", "12986 2 6493", "6493 43 151", "151 151 1" ]
120194	2 19 3163	[ "120194 2 60097", "60097 19 3163", "3163 3163 1" ]
1068308	2 2 409 653	[ "1068308 2 534154", "534154 2 267077", "267077 409 653", "653 653 1" ]
4415015	5 11 80273	[ "4415015 5 883003", "883003 11 80273", "80273 80273 1" ]
1405734	2 3 11 19 19 59	[ "1405734 2 702867", "702867 3 234289", "234289 11 21299", "21299 19 1121", "1121 19 59", "59 59 1" ]
380707	380707	[ "380707 380707 1" ]
980403	3 29 59 191	[ "980403 3 326801", "326801 29 11269", "11269 59 191", "191 191 1" ]
2699503	107 25229	[ "2699503 107 25229", "25229 25229 1" ]
4072649	7 223 2609	[ "4072649 7 581807", "581807 223 2609", "2609 2609 1" ]
1131581	11 102871	[ "1131581 11 102871", "102871 102871 1" ]
49967	29 1723	[ "49967 29 1723", "1723 1723 1" ]
2593742	2 41 47 673	[ "2593742 2 1296871", "1296871 41 31631", "31631 47 673", "673 673 1" ]
1768853	1768853	[ "1768853 1768853 1" ]
4644834	2 3 59 13121	[ "4644834 2 2322417", "2322417 3 774139", "774139 59 13121", "13121 13121 1" ]
3604337	11 327667	[ "3604337 11 327667", "327667 327667 1" ]
1561984	2 2 2 2 2 2 2 12203	[ "1561984 2 780992", "780992 2 390496", "390496 2 195248", "195248 2 97624", "97624 2 48812", "48812 2 24406", "24406 2 12203", "12203 12203 1" ]
3559085	5 711817	[ "3559085 5 711817", "711817 711817 1" ]
4051846	2 2025923	[ "4051846 2 2025923", "2025923 2025923 1" ]
3011489	13 83 2791	[ "3011489 13 231653", "231653 83 2791", "2791 2791 1" ]
2865291	3 11 13 6679	[ "2865291 3 955097", "955097 11 86827", "86827 13 6679", "6679 6679 1" ]
4809935	5 13 73999	[ "4809935 5 961987", "961987 13 73999", "73999 73999 1" ]
4480411	13 107 3221	[ "4480411 13 344647", "344647 107 3221", "3221 3221 1" ]
1391667	3 463889	[ "1391667 3 463889", "463889 463889 1" ]
3327259	13 211 1213	[ "3327259 13 255943", "255943 211 1213", "1213 1213 1" ]
523023	3 313 557	[ "523023 3 174341", "174341 313 557", "557 557 1" ]
1044476	2 2 23 11353	[ "1044476 2 522238", "522238 2 261119", "261119 23 11353", "11353 11353 1" ]

4479276

2 2 3 373273

[ "4479276 2 2239638", "2239638 2 1119819", "1119819 3 373273", "373273 373273 1" ]

1717222

2 13 66047

[ "1717222 2 858611", "858611 13 66047", "66047 66047 1" ]

4672099

[ "4672099 4672099 1" ]

2600974

2 1300487

[ "2600974 2 1300487", "1300487 1300487 1" ]

1904873

53 127 283

[ "1904873 53 35941", "35941 127 283", "283 283 1" ]

3436096

2 2 2 2 2 2 53 1013

[ "3436096 2 1718048", "1718048 2 859024", "859024 2 429512", "429512 2 214756", "214756 2 107378", "107378 2 53689", "53689 53 1013", "1013 1013 1" ]

3520414

2 151 11657

[ "3520414 2 1760207", "1760207 151 11657", "11657 11657 1" ]

3857819

7 7 131 601

[ "3857819 7 551117", "551117 7 78731", "78731 131 601", "601 601 1" ]

4343962

2 7 310283

[ "4343962 2 2171981", "2171981 7 310283", "310283 310283 1" ]

2916449

31 94079

[ "2916449 31 94079", "94079 94079 1" ]

2791875

3 5 5 5 5 1489

[ "2791875 3 930625", "930625 5 186125", "186125 5 37225", "37225 5 7445", "7445 5 1489", "1489 1489 1" ]

4703599

31 151729

[ "4703599 31 151729", "151729 151729 1" ]

3517082

2 1758541

[ "3517082 2 1758541", "1758541 1758541 1" ]

1680171

3 283 1979

[ "1680171 3 560057", "560057 283 1979", "1979 1979 1" ]

62187

3 19 1091

[ "62187 3 20729", "20729 19 1091", "1091 1091 1" ]

3809381

[ "3809381 3809381 1" ]

890429

[ "890429 890429 1" ]

4686526

2 13 17 23 461

[ "4686526 2 2343263", "2343263 13 180251", "180251 17 10603", "10603 23 461", "461 461 1" ]

278485

5 55697

[ "278485 5 55697", "55697 55697 1" ]

1555318

2 353 2203

[ "1555318 2 777659", "777659 353 2203", "2203 2203 1" ]

4830509

349 13841

[ "4830509 349 13841", "13841 13841 1" ]

2818611

3 3 3 104393

[ "2818611 3 939537", "939537 3 313179", "313179 3 104393", "104393 104393 1" ]

457663

59 7757

[ "457663 59 7757", "7757 7757 1" ]

2089484

2 2 522371

[ "2089484 2 1044742", "1044742 2 522371", "522371 522371 1" ]

3998059

13 307543

[ "3998059 13 307543", "307543 307543 1" ]

312950

2 5 5 11 569

[ "312950 2 156475", "156475 5 31295", "31295 5 6259", "6259 11 569", "569 569 1" ]

1393741

53 26297

[ "1393741 53 26297", "26297 26297 1" ]

2886411

3 11 47 1861

[ "2886411 3 962137", "962137 11 87467", "87467 47 1861", "1861 1861 1" ]

806120

2 2 2 5 7 2879

[ "806120 2 403060", "403060 2 201530", "201530 2 100765", "100765 5 20153", "20153 7 2879", "2879 2879 1" ]

467510

2 5 46751

[ "467510 2 233755", "233755 5 46751", "46751 46751 1" ]

4527035

5 19 47653

[ "4527035 5 905407", "905407 19 47653", "47653 47653 1" ]

2672752

2 2 2 2 167047

[ "2672752 2 1336376", "1336376 2 668188", "668188 2 334094", "334094 2 167047", "167047 167047 1" ]

1322401

97 13633

[ "1322401 97 13633", "13633 13633 1" ]

3009506

2 37 67 607

[ "3009506 2 1504753", "1504753 37 40669", "40669 67 607", "607 607 1" ]

4746163

[ "4746163 4746163 1" ]

4457797

37 211 571

[ "4457797 37 120481", "120481 211 571", "571 571 1" ]

3248192

2 2 2 2 2 2 50753

[ "3248192 2 1624096", "1624096 2 812048", "812048 2 406024", "406024 2 203012", "203012 2 101506", "101506 2 50753", "50753 50753 1" ]

200875

5 5 5 1607

[ "200875 5 40175", "40175 5 8035", "8035 5 1607", "1607 1607 1" ]

470053

31 59 257

[ "470053 31 15163", "15163 59 257", "257 257 1" ]

1588062

2 3 7 37811

[ "1588062 2 794031", "794031 3 264677", "264677 7 37811", "37811 37811 1" ]

2947514

2 197 7481

[ "2947514 2 1473757", "1473757 197 7481", "7481 7481 1" ]

315328

2 2 2 2 2 2 13 379

[ "315328 2 157664", "157664 2 78832", "78832 2 39416", "39416 2 19708", "19708 2 9854", "9854 2 4927", "4927 13 379", "379 379 1" ]

2876934

2 3 479489

[ "2876934 2 1438467", "1438467 3 479489", "479489 479489 1" ]

2283833

[ "2283833 2283833 1" ]

521881

[ "521881 521881 1" ]

1985838

2 3 17 19469

[ "1985838 2 992919", "992919 3 330973", "330973 17 19469", "19469 19469 1" ]

535206

2 3 7 12743

[ "535206 2 267603", "267603 3 89201", "89201 7 12743", "12743 12743 1" ]

3760188

2 2 3 47 59 113

[ "3760188 2 1880094", "1880094 2 940047", "940047 3 313349", "313349 47 6667", "6667 59 113", "113 113 1" ]

1370588

2 2 342647

[ "1370588 2 685294", "685294 2 342647", "342647 342647 1" ]

4706792

2 2 2 31 18979

[ "4706792 2 2353396", "2353396 2 1176698", "1176698 2 588349", "588349 31 18979", "18979 18979 1" ]

131297

[ "131297 131297 1" ]

1346567

[ "1346567 1346567 1" ]

1824572

2 2 349 1307

[ "1824572 2 912286", "912286 2 456143", "456143 349 1307", "1307 1307 1" ]

467049

3 11 14153

[ "467049 3 155683", "155683 11 14153", "14153 14153 1" ]

2222534

2 103 10789

[ "2222534 2 1111267", "1111267 103 10789", "10789 10789 1" ]

4403812

2 2 7 157279

[ "4403812 2 2201906", "2201906 2 1100953", "1100953 7 157279", "157279 157279 1" ]

4492283

67 67049

[ "4492283 67 67049", "67049 67049 1" ]

1921565

5 19 113 179

[ "1921565 5 384313", "384313 19 20227", "20227 113 179", "179 179 1" ]

2384825

5 5 95393

[ "2384825 5 476965", "476965 5 95393", "95393 95393 1" ]

1635332

2 2 17 24049

[ "1635332 2 817666", "817666 2 408833", "408833 17 24049", "24049 24049 1" ]

4317140

2 2 5 215857

[ "4317140 2 2158570", "2158570 2 1079285", "1079285 5 215857", "215857 215857 1" ]

4535120

2 2 2 2 5 83 683

[ "4535120 2 2267560", "2267560 2 1133780", "1133780 2 566890", "566890 2 283445", "283445 5 56689", "56689 83 683", "683 683 1" ]

608844

2 2 3 113 449

[ "608844 2 304422", "304422 2 152211", "152211 3 50737", "50737 113 449", "449 449 1" ]

4443574

2 67 33161

[ "4443574 2 2221787", "2221787 67 33161", "33161 33161 1" ]

3352967

[ "3352967 3352967 1" ]

662242

2 7 47303

[ "662242 2 331121", "331121 7 47303", "47303 47303 1" ]

3735576

2 2 2 3 3 13 13 307

[ "3735576 2 1867788", "1867788 2 933894", "933894 2 466947", "466947 3 155649", "155649 3 51883", "51883 13 3991", "3991 13 307", "307 307 1" ]

115031

7 16433

[ "115031 7 16433", "16433 16433 1" ]

2742129

3 3 13 23 1019

[ "2742129 3 914043", "914043 3 304681", "304681 13 23437", "23437 23 1019", "1019 1019 1" ]

1898372

2 2 7 151 449

[ "1898372 2 949186", "949186 2 474593", "474593 7 67799", "67799 151 449", "449 449 1" ]

2512973

131 19183

[ "2512973 131 19183", "19183 19183 1" ]

4052163

3 23 58727

[ "4052163 3 1350721", "1350721 23 58727", "58727 58727 1" ]

3820413

3 1273471

[ "3820413 3 1273471", "1273471 1273471 1" ]

626076

2 2 3 3 3 11 17 31

[ "626076 2 313038", "313038 2 156519", "156519 3 52173", "52173 3 17391", "17391 3 5797", "5797 11 527", "527 17 31", "31 31 1" ]

831104

2 2 2 2 2 2 2 43 151

[ "831104 2 415552", "415552 2 207776", "207776 2 103888", "103888 2 51944", "51944 2 25972", "25972 2 12986", "12986 2 6493", "6493 43 151", "151 151 1" ]

120194

2 19 3163

[ "120194 2 60097", "60097 19 3163", "3163 3163 1" ]

1068308

2 2 409 653

[ "1068308 2 534154", "534154 2 267077", "267077 409 653", "653 653 1" ]

4415015

5 11 80273

[ "4415015 5 883003", "883003 11 80273", "80273 80273 1" ]

1405734

2 3 11 19 19 59

[ "1405734 2 702867", "702867 3 234289", "234289 11 21299", "21299 19 1121", "1121 19 59", "59 59 1" ]

380707

[ "380707 380707 1" ]

980403

3 29 59 191

[ "980403 3 326801", "326801 29 11269", "11269 59 191", "191 191 1" ]

2699503

107 25229

[ "2699503 107 25229", "25229 25229 1" ]

4072649

7 223 2609

[ "4072649 7 581807", "581807 223 2609", "2609 2609 1" ]

1131581

11 102871

[ "1131581 11 102871", "102871 102871 1" ]

49967

29 1723

[ "49967 29 1723", "1723 1723 1" ]

2593742

2 41 47 673

[ "2593742 2 1296871", "1296871 41 31631", "31631 47 673", "673 673 1" ]

1768853

[ "1768853 1768853 1" ]

4644834

2 3 59 13121

[ "4644834 2 2322417", "2322417 3 774139", "774139 59 13121", "13121 13121 1" ]

3604337

11 327667

[ "3604337 11 327667", "327667 327667 1" ]

1561984

2 2 2 2 2 2 2 12203

[ "1561984 2 780992", "780992 2 390496", "390496 2 195248", "195248 2 97624", "97624 2 48812", "48812 2 24406", "24406 2 12203", "12203 12203 1" ]

3559085

5 711817

[ "3559085 5 711817", "711817 711817 1" ]

4051846

2 2025923

[ "4051846 2 2025923", "2025923 2025923 1" ]

3011489

13 83 2791

[ "3011489 13 231653", "231653 83 2791", "2791 2791 1" ]

2865291

3 11 13 6679

[ "2865291 3 955097", "955097 11 86827", "86827 13 6679", "6679 6679 1" ]

4809935

5 13 73999

[ "4809935 5 961987", "961987 13 73999", "73999 73999 1" ]

4480411

13 107 3221

[ "4480411 13 344647", "344647 107 3221", "3221 3221 1" ]

1391667

3 463889

[ "1391667 3 463889", "463889 463889 1" ]

3327259

13 211 1213

[ "3327259 13 255943", "255943 211 1213", "1213 1213 1" ]

523023

3 313 557

[ "523023 3 174341", "174341 313 557", "557 557 1" ]

1044476

2 2 23 11353

[ "1044476 2 522238", "522238 2 261119", "261119 23 11353", "11353 11353 1" ]