yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
3934389	3 223 5881	[ "3934389 3 1311463", "1311463 223 5881", "5881 5881 1" ]
835198	2 7 13 13 353	[ "835198 2 417599", "417599 7 59657", "59657 13 4589", "4589 13 353", "353 353 1" ]
1872919	1872919	[ "1872919 1872919 1" ]
4370927	11 397357	[ "4370927 11 397357", "397357 397357 1" ]
1171560	2 2 2 3 5 13 751	[ "1171560 2 585780", "585780 2 292890", "292890 2 146445", "146445 3 48815", "48815 5 9763", "9763 13 751", "751 751 1" ]
1544845	5 79 3911	[ "1544845 5 308969", "308969 79 3911", "3911 3911 1" ]
103911	3 19 1823	[ "103911 3 34637", "34637 19 1823", "1823 1823 1" ]
4198900	2 2 5 5 199 211	[ "4198900 2 2099450", "2099450 2 1049725", "1049725 5 209945", "209945 5 41989", "41989 199 211", "211 211 1" ]
1496218	2 457 1637	[ "1496218 2 748109", "748109 457 1637", "1637 1637 1" ]
1377543	3 459181	[ "1377543 3 459181", "459181 459181 1" ]
4742622	2 3 3 173 1523	[ "4742622 2 2371311", "2371311 3 790437", "790437 3 263479", "263479 173 1523", "1523 1523 1" ]
154703	67 2309	[ "154703 67 2309", "2309 2309 1" ]
2149731	3 3 238859	[ "2149731 3 716577", "716577 3 238859", "238859 238859 1" ]
1082944	2 2 2 2 2 2 16921	[ "1082944 2 541472", "541472 2 270736", "270736 2 135368", "135368 2 67684", "67684 2 33842", "33842 2 16921", "16921 16921 1" ]
2171084	2 2 542771	[ "2171084 2 1085542", "1085542 2 542771", "542771 542771 1" ]
449254	2 13 37 467	[ "449254 2 224627", "224627 13 17279", "17279 37 467", "467 467 1" ]
20348	2 2 5087	[ "20348 2 10174", "10174 2 5087", "5087 5087 1" ]
4815474	2 3 19 53 797	[ "4815474 2 2407737", "2407737 3 802579", "802579 19 42241", "42241 53 797", "797 797 1" ]
1230943	7 41 4289	[ "1230943 7 175849", "175849 41 4289", "4289 4289 1" ]
3849770	2 5 47 8191	[ "3849770 2 1924885", "1924885 5 384977", "384977 47 8191", "8191 8191 1" ]
3072118	2 7 219437	[ "3072118 2 1536059", "1536059 7 219437", "219437 219437 1" ]
3303282	2 3 293 1879	[ "3303282 2 1651641", "1651641 3 550547", "550547 293 1879", "1879 1879 1" ]
3654893	11 332263	[ "3654893 11 332263", "332263 332263 1" ]
4134251	11 375841	[ "4134251 11 375841", "375841 375841 1" ]
2710053	3 3 127 2371	[ "2710053 3 903351", "903351 3 301117", "301117 127 2371", "2371 2371 1" ]
3934943	3934943	[ "3934943 3934943 1" ]
378866	2 189433	[ "378866 2 189433", "189433 189433 1" ]
672193	672193	[ "672193 672193 1" ]
3629000	2 2 2 5 5 5 19 191	[ "3629000 2 1814500", "1814500 2 907250", "907250 2 453625", "453625 5 90725", "90725 5 18145", "18145 5 3629", "3629 19 191", "191 191 1" ]
1220364	2 2 3 3 109 311	[ "1220364 2 610182", "610182 2 305091", "305091 3 101697", "101697 3 33899", "33899 109 311", "311 311 1" ]
4419578	2 2209789	[ "4419578 2 2209789", "2209789 2209789 1" ]
3024916	2 2 67 11287	[ "3024916 2 1512458", "1512458 2 756229", "756229 67 11287", "11287 11287 1" ]
3268899	3 3 363211	[ "3268899 3 1089633", "1089633 3 363211", "363211 363211 1" ]
1363826	2 681913	[ "1363826 2 681913", "681913 681913 1" ]
717850	2 5 5 7 7 293	[ "717850 2 358925", "358925 5 71785", "71785 5 14357", "14357 7 2051", "2051 7 293", "293 293 1" ]
381693	3 13 9787	[ "381693 3 127231", "127231 13 9787", "9787 9787 1" ]
2497984	2 2 2 2 2 2 23 1697	[ "2497984 2 1248992", "1248992 2 624496", "624496 2 312248", "312248 2 156124", "156124 2 78062", "78062 2 39031", "39031 23 1697", "1697 1697 1" ]
2328741	3 3 353 733	[ "2328741 3 776247", "776247 3 258749", "258749 353 733", "733 733 1" ]
1587135	3 5 11 9619	[ "1587135 3 529045", "529045 5 105809", "105809 11 9619", "9619 9619 1" ]
1093205	5 218641	[ "1093205 5 218641", "218641 218641 1" ]
2261220	2 2 3 5 13 13 223	[ "2261220 2 1130610", "1130610 2 565305", "565305 3 188435", "188435 5 37687", "37687 13 2899", "2899 13 223", "223 223 1" ]
3345864	2 2 2 3 109 1279	[ "3345864 2 1672932", "1672932 2 836466", "836466 2 418233", "418233 3 139411", "139411 109 1279", "1279 1279 1" ]
3411437	37 137 673	[ "3411437 37 92201", "92201 137 673", "673 673 1" ]
3904655	5 780931	[ "3904655 5 780931", "780931 780931 1" ]
2008117	53 37889	[ "2008117 53 37889", "37889 37889 1" ]
3389200	2 2 2 2 5 5 37 229	[ "3389200 2 1694600", "1694600 2 847300", "847300 2 423650", "423650 2 211825", "211825 5 42365", "42365 5 8473", "8473 37 229", "229 229 1" ]
1670742	2 3 3 101 919	[ "1670742 2 835371", "835371 3 278457", "278457 3 92819", "92819 101 919", "919 919 1" ]
1459014	2 3 241 1009	[ "1459014 2 729507", "729507 3 243169", "243169 241 1009", "1009 1009 1" ]
4033020	2 2 3 5 67217	[ "4033020 2 2016510", "2016510 2 1008255", "1008255 3 336085", "336085 5 67217", "67217 67217 1" ]
3134943	3 3 3 3 3 7 19 97	[ "3134943 3 1044981", "1044981 3 348327", "348327 3 116109", "116109 3 38703", "38703 3 12901", "12901 7 1843", "1843 19 97", "97 97 1" ]
51119	17 31 97	[ "51119 17 3007", "3007 31 97", "97 97 1" ]
1147253	1147253	[ "1147253 1147253 1" ]
1324693	613 2161	[ "1324693 613 2161", "2161 2161 1" ]
3447043	3447043	[ "3447043 3447043 1" ]
3269700	2 2 3 3 3 5 5 7 173	[ "3269700 2 1634850", "1634850 2 817425", "817425 3 272475", "272475 3 90825", "90825 3 30275", "30275 5 6055", "6055 5 1211", "1211 7 173", "173 173 1" ]
887531	523 1697	[ "887531 523 1697", "1697 1697 1" ]
95579	11 8689	[ "95579 11 8689", "8689 8689 1" ]
3535802	2 283 6247	[ "3535802 2 1767901", "1767901 283 6247", "6247 6247 1" ]
336255	3 5 29 773	[ "336255 3 112085", "112085 5 22417", "22417 29 773", "773 773 1" ]
4772662	2 47 50773	[ "4772662 2 2386331", "2386331 47 50773", "50773 50773 1" ]
1863692	2 2 53 59 149	[ "1863692 2 931846", "931846 2 465923", "465923 53 8791", "8791 59 149", "149 149 1" ]
3678079	47 139 563	[ "3678079 47 78257", "78257 139 563", "563 563 1" ]
1034615	5 206923	[ "1034615 5 206923", "206923 206923 1" ]
3727793	3727793	[ "3727793 3727793 1" ]
2097059	137 15307	[ "2097059 137 15307", "15307 15307 1" ]
4687255	5 59 15889	[ "4687255 5 937451", "937451 59 15889", "15889 15889 1" ]
4637257	277 16741	[ "4637257 277 16741", "16741 16741 1" ]
1838143	1838143	[ "1838143 1838143 1" ]
3771815	5 487 1549	[ "3771815 5 754363", "754363 487 1549", "1549 1549 1" ]
423096	2 2 2 3 17 17 61	[ "423096 2 211548", "211548 2 105774", "105774 2 52887", "52887 3 17629", "17629 17 1037", "1037 17 61", "61 61 1" ]
1197709	1197709	[ "1197709 1197709 1" ]
611647	37 61 271	[ "611647 37 16531", "16531 61 271", "271 271 1" ]
1738281	3 579427	[ "1738281 3 579427", "579427 579427 1" ]
4097957	4097957	[ "4097957 4097957 1" ]
2523767	23 197 557	[ "2523767 23 109729", "109729 197 557", "557 557 1" ]
4312494	2 3 3 3 79861	[ "4312494 2 2156247", "2156247 3 718749", "718749 3 239583", "239583 3 79861", "79861 79861 1" ]
49824	2 2 2 2 2 3 3 173	[ "49824 2 24912", "24912 2 12456", "12456 2 6228", "6228 2 3114", "3114 2 1557", "1557 3 519", "519 3 173", "173 173 1" ]
2358290	2 5 11 11 1949	[ "2358290 2 1179145", "1179145 5 235829", "235829 11 21439", "21439 11 1949", "1949 1949 1" ]
623253	3 103 2017	[ "623253 3 207751", "207751 103 2017", "2017 2017 1" ]
1896496	2 2 2 2 7 7 41 59	[ "1896496 2 948248", "948248 2 474124", "474124 2 237062", "237062 2 118531", "118531 7 16933", "16933 7 2419", "2419 41 59", "59 59 1" ]
3697176	2 2 2 3 7 59 373	[ "3697176 2 1848588", "1848588 2 924294", "924294 2 462147", "462147 3 154049", "154049 7 22007", "22007 59 373", "373 373 1" ]
4331342	2 2165671	[ "4331342 2 2165671", "2165671 2165671 1" ]
4417992	2 2 2 3 3 43 1427	[ "4417992 2 2208996", "2208996 2 1104498", "1104498 2 552249", "552249 3 184083", "184083 3 61361", "61361 43 1427", "1427 1427 1" ]
3041789	3041789	[ "3041789 3041789 1" ]
2520685	5 23 23 953	[ "2520685 5 504137", "504137 23 21919", "21919 23 953", "953 953 1" ]
3376531	101 101 331	[ "3376531 101 33431", "33431 101 331", "331 331 1" ]
1969972	2 2 587 839	[ "1969972 2 984986", "984986 2 492493", "492493 587 839", "839 839 1" ]
1851797	19 97463	[ "1851797 19 97463", "97463 97463 1" ]
3330915	3 5 7 31723	[ "3330915 3 1110305", "1110305 5 222061", "222061 7 31723", "31723 31723 1" ]
792968	2 2 2 11 9011	[ "792968 2 396484", "396484 2 198242", "198242 2 99121", "99121 11 9011", "9011 9011 1" ]
4366743	3 149 9769	[ "4366743 3 1455581", "1455581 149 9769", "9769 9769 1" ]
1473903	3 3 3 79 691	[ "1473903 3 491301", "491301 3 163767", "163767 3 54589", "54589 79 691", "691 691 1" ]
4006582	2 29 37 1867	[ "4006582 2 2003291", "2003291 29 69079", "69079 37 1867", "1867 1867 1" ]
2543145	3 5 11 15413	[ "2543145 3 847715", "847715 5 169543", "169543 11 15413", "15413 15413 1" ]
2812153	2812153	[ "2812153 2812153 1" ]
2589256	2 2 2 317 1021	[ "2589256 2 1294628", "1294628 2 647314", "647314 2 323657", "323657 317 1021", "1021 1021 1" ]
1843373	7 71 3709	[ "1843373 7 263339", "263339 71 3709", "3709 3709 1" ]
2909466	2 3 3 3 7 43 179	[ "2909466 2 1454733", "1454733 3 484911", "484911 3 161637", "161637 3 53879", "53879 7 7697", "7697 43 179", "179 179 1" ]
4698683	11 79 5407	[ "4698683 11 427153", "427153 79 5407", "5407 5407 1" ]
3808652	2 2 952163	[ "3808652 2 1904326", "1904326 2 952163", "952163 952163 1" ]

3934389

3 223 5881

[ "3934389 3 1311463", "1311463 223 5881", "5881 5881 1" ]

835198

2 7 13 13 353

[ "835198 2 417599", "417599 7 59657", "59657 13 4589", "4589 13 353", "353 353 1" ]

1872919

[ "1872919 1872919 1" ]

4370927

11 397357

[ "4370927 11 397357", "397357 397357 1" ]

1171560

2 2 2 3 5 13 751

[ "1171560 2 585780", "585780 2 292890", "292890 2 146445", "146445 3 48815", "48815 5 9763", "9763 13 751", "751 751 1" ]

1544845

5 79 3911

[ "1544845 5 308969", "308969 79 3911", "3911 3911 1" ]

103911

3 19 1823

[ "103911 3 34637", "34637 19 1823", "1823 1823 1" ]

4198900

2 2 5 5 199 211

[ "4198900 2 2099450", "2099450 2 1049725", "1049725 5 209945", "209945 5 41989", "41989 199 211", "211 211 1" ]

1496218

2 457 1637

[ "1496218 2 748109", "748109 457 1637", "1637 1637 1" ]

1377543

3 459181

[ "1377543 3 459181", "459181 459181 1" ]

4742622

2 3 3 173 1523

[ "4742622 2 2371311", "2371311 3 790437", "790437 3 263479", "263479 173 1523", "1523 1523 1" ]

154703

67 2309

[ "154703 67 2309", "2309 2309 1" ]

2149731

3 3 238859

[ "2149731 3 716577", "716577 3 238859", "238859 238859 1" ]

1082944

2 2 2 2 2 2 16921

[ "1082944 2 541472", "541472 2 270736", "270736 2 135368", "135368 2 67684", "67684 2 33842", "33842 2 16921", "16921 16921 1" ]

2171084

2 2 542771

[ "2171084 2 1085542", "1085542 2 542771", "542771 542771 1" ]

449254

2 13 37 467

[ "449254 2 224627", "224627 13 17279", "17279 37 467", "467 467 1" ]

20348

2 2 5087

[ "20348 2 10174", "10174 2 5087", "5087 5087 1" ]

4815474

2 3 19 53 797

[ "4815474 2 2407737", "2407737 3 802579", "802579 19 42241", "42241 53 797", "797 797 1" ]

1230943

7 41 4289

[ "1230943 7 175849", "175849 41 4289", "4289 4289 1" ]

3849770

2 5 47 8191

[ "3849770 2 1924885", "1924885 5 384977", "384977 47 8191", "8191 8191 1" ]

3072118

2 7 219437

[ "3072118 2 1536059", "1536059 7 219437", "219437 219437 1" ]

3303282

2 3 293 1879

[ "3303282 2 1651641", "1651641 3 550547", "550547 293 1879", "1879 1879 1" ]

3654893

11 332263

[ "3654893 11 332263", "332263 332263 1" ]

4134251

11 375841

[ "4134251 11 375841", "375841 375841 1" ]

2710053

3 3 127 2371

[ "2710053 3 903351", "903351 3 301117", "301117 127 2371", "2371 2371 1" ]

3934943

[ "3934943 3934943 1" ]

378866

2 189433

[ "378866 2 189433", "189433 189433 1" ]

672193

[ "672193 672193 1" ]

3629000

2 2 2 5 5 5 19 191

[ "3629000 2 1814500", "1814500 2 907250", "907250 2 453625", "453625 5 90725", "90725 5 18145", "18145 5 3629", "3629 19 191", "191 191 1" ]

1220364

2 2 3 3 109 311

[ "1220364 2 610182", "610182 2 305091", "305091 3 101697", "101697 3 33899", "33899 109 311", "311 311 1" ]

4419578

2 2209789

[ "4419578 2 2209789", "2209789 2209789 1" ]

3024916

2 2 67 11287

[ "3024916 2 1512458", "1512458 2 756229", "756229 67 11287", "11287 11287 1" ]

3268899

3 3 363211

[ "3268899 3 1089633", "1089633 3 363211", "363211 363211 1" ]

1363826

2 681913

[ "1363826 2 681913", "681913 681913 1" ]

717850

2 5 5 7 7 293

[ "717850 2 358925", "358925 5 71785", "71785 5 14357", "14357 7 2051", "2051 7 293", "293 293 1" ]

381693

3 13 9787

[ "381693 3 127231", "127231 13 9787", "9787 9787 1" ]

2497984

2 2 2 2 2 2 23 1697

[ "2497984 2 1248992", "1248992 2 624496", "624496 2 312248", "312248 2 156124", "156124 2 78062", "78062 2 39031", "39031 23 1697", "1697 1697 1" ]

2328741

3 3 353 733

[ "2328741 3 776247", "776247 3 258749", "258749 353 733", "733 733 1" ]

1587135

3 5 11 9619

[ "1587135 3 529045", "529045 5 105809", "105809 11 9619", "9619 9619 1" ]

1093205

5 218641

[ "1093205 5 218641", "218641 218641 1" ]

2261220

2 2 3 5 13 13 223

[ "2261220 2 1130610", "1130610 2 565305", "565305 3 188435", "188435 5 37687", "37687 13 2899", "2899 13 223", "223 223 1" ]

3345864

2 2 2 3 109 1279

[ "3345864 2 1672932", "1672932 2 836466", "836466 2 418233", "418233 3 139411", "139411 109 1279", "1279 1279 1" ]

3411437

37 137 673

[ "3411437 37 92201", "92201 137 673", "673 673 1" ]

3904655

5 780931

[ "3904655 5 780931", "780931 780931 1" ]

2008117

53 37889

[ "2008117 53 37889", "37889 37889 1" ]

3389200

2 2 2 2 5 5 37 229

[ "3389200 2 1694600", "1694600 2 847300", "847300 2 423650", "423650 2 211825", "211825 5 42365", "42365 5 8473", "8473 37 229", "229 229 1" ]

1670742

2 3 3 101 919

[ "1670742 2 835371", "835371 3 278457", "278457 3 92819", "92819 101 919", "919 919 1" ]

1459014

2 3 241 1009

[ "1459014 2 729507", "729507 3 243169", "243169 241 1009", "1009 1009 1" ]

4033020

2 2 3 5 67217

[ "4033020 2 2016510", "2016510 2 1008255", "1008255 3 336085", "336085 5 67217", "67217 67217 1" ]

3134943

3 3 3 3 3 7 19 97

[ "3134943 3 1044981", "1044981 3 348327", "348327 3 116109", "116109 3 38703", "38703 3 12901", "12901 7 1843", "1843 19 97", "97 97 1" ]

51119

17 31 97

[ "51119 17 3007", "3007 31 97", "97 97 1" ]

1147253

[ "1147253 1147253 1" ]

1324693

613 2161

[ "1324693 613 2161", "2161 2161 1" ]

3447043

[ "3447043 3447043 1" ]

3269700

2 2 3 3 3 5 5 7 173

[ "3269700 2 1634850", "1634850 2 817425", "817425 3 272475", "272475 3 90825", "90825 3 30275", "30275 5 6055", "6055 5 1211", "1211 7 173", "173 173 1" ]

887531

523 1697

[ "887531 523 1697", "1697 1697 1" ]

95579

11 8689

[ "95579 11 8689", "8689 8689 1" ]

3535802

2 283 6247

[ "3535802 2 1767901", "1767901 283 6247", "6247 6247 1" ]

336255

3 5 29 773

[ "336255 3 112085", "112085 5 22417", "22417 29 773", "773 773 1" ]

4772662

2 47 50773

[ "4772662 2 2386331", "2386331 47 50773", "50773 50773 1" ]

1863692

2 2 53 59 149

[ "1863692 2 931846", "931846 2 465923", "465923 53 8791", "8791 59 149", "149 149 1" ]

3678079

47 139 563

[ "3678079 47 78257", "78257 139 563", "563 563 1" ]

1034615

5 206923

[ "1034615 5 206923", "206923 206923 1" ]

3727793

[ "3727793 3727793 1" ]

2097059

137 15307

[ "2097059 137 15307", "15307 15307 1" ]

4687255

5 59 15889

[ "4687255 5 937451", "937451 59 15889", "15889 15889 1" ]

4637257

277 16741

[ "4637257 277 16741", "16741 16741 1" ]

1838143

[ "1838143 1838143 1" ]

3771815

5 487 1549

[ "3771815 5 754363", "754363 487 1549", "1549 1549 1" ]

423096

2 2 2 3 17 17 61

[ "423096 2 211548", "211548 2 105774", "105774 2 52887", "52887 3 17629", "17629 17 1037", "1037 17 61", "61 61 1" ]

1197709

[ "1197709 1197709 1" ]

611647

37 61 271

[ "611647 37 16531", "16531 61 271", "271 271 1" ]

1738281

3 579427

[ "1738281 3 579427", "579427 579427 1" ]

4097957

[ "4097957 4097957 1" ]

2523767

23 197 557

[ "2523767 23 109729", "109729 197 557", "557 557 1" ]

4312494

2 3 3 3 79861

[ "4312494 2 2156247", "2156247 3 718749", "718749 3 239583", "239583 3 79861", "79861 79861 1" ]

49824

2 2 2 2 2 3 3 173

[ "49824 2 24912", "24912 2 12456", "12456 2 6228", "6228 2 3114", "3114 2 1557", "1557 3 519", "519 3 173", "173 173 1" ]

2358290

2 5 11 11 1949

[ "2358290 2 1179145", "1179145 5 235829", "235829 11 21439", "21439 11 1949", "1949 1949 1" ]

623253

3 103 2017

[ "623253 3 207751", "207751 103 2017", "2017 2017 1" ]

1896496

2 2 2 2 7 7 41 59

[ "1896496 2 948248", "948248 2 474124", "474124 2 237062", "237062 2 118531", "118531 7 16933", "16933 7 2419", "2419 41 59", "59 59 1" ]

3697176

2 2 2 3 7 59 373

[ "3697176 2 1848588", "1848588 2 924294", "924294 2 462147", "462147 3 154049", "154049 7 22007", "22007 59 373", "373 373 1" ]

4331342

2 2165671

[ "4331342 2 2165671", "2165671 2165671 1" ]

4417992

2 2 2 3 3 43 1427

[ "4417992 2 2208996", "2208996 2 1104498", "1104498 2 552249", "552249 3 184083", "184083 3 61361", "61361 43 1427", "1427 1427 1" ]

3041789

[ "3041789 3041789 1" ]

2520685

5 23 23 953

[ "2520685 5 504137", "504137 23 21919", "21919 23 953", "953 953 1" ]

3376531

101 101 331

[ "3376531 101 33431", "33431 101 331", "331 331 1" ]

1969972

2 2 587 839

[ "1969972 2 984986", "984986 2 492493", "492493 587 839", "839 839 1" ]

1851797

19 97463

[ "1851797 19 97463", "97463 97463 1" ]

3330915

3 5 7 31723

[ "3330915 3 1110305", "1110305 5 222061", "222061 7 31723", "31723 31723 1" ]

792968

2 2 2 11 9011

[ "792968 2 396484", "396484 2 198242", "198242 2 99121", "99121 11 9011", "9011 9011 1" ]

4366743

3 149 9769

[ "4366743 3 1455581", "1455581 149 9769", "9769 9769 1" ]

1473903

3 3 3 79 691

[ "1473903 3 491301", "491301 3 163767", "163767 3 54589", "54589 79 691", "691 691 1" ]

4006582

2 29 37 1867

[ "4006582 2 2003291", "2003291 29 69079", "69079 37 1867", "1867 1867 1" ]

2543145

3 5 11 15413

[ "2543145 3 847715", "847715 5 169543", "169543 11 15413", "15413 15413 1" ]

2812153

[ "2812153 2812153 1" ]

2589256

2 2 2 317 1021

[ "2589256 2 1294628", "1294628 2 647314", "647314 2 323657", "323657 317 1021", "1021 1021 1" ]

1843373

7 71 3709

[ "1843373 7 263339", "263339 71 3709", "3709 3709 1" ]

2909466

2 3 3 3 7 43 179

[ "2909466 2 1454733", "1454733 3 484911", "484911 3 161637", "161637 3 53879", "53879 7 7697", "7697 43 179", "179 179 1" ]

4698683

11 79 5407

[ "4698683 11 427153", "427153 79 5407", "5407 5407 1" ]

3808652

2 2 952163

[ "3808652 2 1904326", "1904326 2 952163", "952163 952163 1" ]