yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1120686	2 3 7 26683	[ "1120686 2 560343", "560343 3 186781", "186781 7 26683", "26683 26683 1" ]
2158306	2 1079153	[ "2158306 2 1079153", "1079153 1079153 1" ]
4233157	419 10103	[ "4233157 419 10103", "10103 10103 1" ]
4564045	5 912809	[ "4564045 5 912809", "912809 912809 1" ]
2050132	2 2 7 17 59 73	[ "2050132 2 1025066", "1025066 2 512533", "512533 7 73219", "73219 17 4307", "4307 59 73", "73 73 1" ]
527062	2 31 8501	[ "527062 2 263531", "263531 31 8501", "8501 8501 1" ]
4999807	191 26177	[ "4999807 191 26177", "26177 26177 1" ]
1265745	3 5 13 6491	[ "1265745 3 421915", "421915 5 84383", "84383 13 6491", "6491 6491 1" ]
3912311	13 257 1171	[ "3912311 13 300947", "300947 257 1171", "1171 1171 1" ]
1861845	3 5 124123	[ "1861845 3 620615", "620615 5 124123", "124123 124123 1" ]
846768	2 2 2 2 3 13 23 59	[ "846768 2 423384", "423384 2 211692", "211692 2 105846", "105846 2 52923", "52923 3 17641", "17641 13 1357", "1357 23 59", "59 59 1" ]
1053717	3 7 50177	[ "1053717 3 351239", "351239 7 50177", "50177 50177 1" ]
1213700	2 2 5 5 53 229	[ "1213700 2 606850", "606850 2 303425", "303425 5 60685", "60685 5 12137", "12137 53 229", "229 229 1" ]
914861	914861	[ "914861 914861 1" ]
4349681	7 7 29 3061	[ "4349681 7 621383", "621383 7 88769", "88769 29 3061", "3061 3061 1" ]
2133335	5 131 3257	[ "2133335 5 426667", "426667 131 3257", "3257 3257 1" ]
2491739	79 31541	[ "2491739 79 31541", "31541 31541 1" ]
227592	2 2 2 3 3 29 109	[ "227592 2 113796", "113796 2 56898", "56898 2 28449", "28449 3 9483", "9483 3 3161", "3161 29 109", "109 109 1" ]
140024	2 2 2 23 761	[ "140024 2 70012", "70012 2 35006", "35006 2 17503", "17503 23 761", "761 761 1" ]
2876786	2 11 43 3041	[ "2876786 2 1438393", "1438393 11 130763", "130763 43 3041", "3041 3041 1" ]
4464379	4464379	[ "4464379 4464379 1" ]
256947	3 41 2089	[ "256947 3 85649", "85649 41 2089", "2089 2089 1" ]
1865797	31 139 433	[ "1865797 31 60187", "60187 139 433", "433 433 1" ]
3335596	2 2 11 41 43 43	[ "3335596 2 1667798", "1667798 2 833899", "833899 11 75809", "75809 41 1849", "1849 43 43", "43 43 1" ]
2931000	2 2 2 3 5 5 5 977	[ "2931000 2 1465500", "1465500 2 732750", "732750 2 366375", "366375 3 122125", "122125 5 24425", "24425 5 4885", "4885 5 977", "977 977 1" ]
3126059	71 44029	[ "3126059 71 44029", "44029 44029 1" ]
1016293	199 5107	[ "1016293 199 5107", "5107 5107 1" ]
2138806	2 41 26083	[ "2138806 2 1069403", "1069403 41 26083", "26083 26083 1" ]
4410453	3 1470151	[ "4410453 3 1470151", "1470151 1470151 1" ]
3338182	2 1669091	[ "3338182 2 1669091", "1669091 1669091 1" ]
3945413	3945413	[ "3945413 3945413 1" ]
1724999	1724999	[ "1724999 1724999 1" ]
2569275	3 3 5 5 19 601	[ "2569275 3 856425", "856425 3 285475", "285475 5 57095", "57095 5 11419", "11419 19 601", "601 601 1" ]
1175999	11 11 9719	[ "1175999 11 106909", "106909 11 9719", "9719 9719 1" ]
1060724	2 2 7 43 881	[ "1060724 2 530362", "530362 2 265181", "265181 7 37883", "37883 43 881", "881 881 1" ]
1736101	1736101	[ "1736101 1736101 1" ]
1731933	3 3 7 37 743	[ "1731933 3 577311", "577311 3 192437", "192437 7 27491", "27491 37 743", "743 743 1" ]
3234139	109 29671	[ "3234139 109 29671", "29671 29671 1" ]
395402	2 7 61 463	[ "395402 2 197701", "197701 7 28243", "28243 61 463", "463 463 1" ]
1370339	827 1657	[ "1370339 827 1657", "1657 1657 1" ]
3960670	2 5 7 7 59 137	[ "3960670 2 1980335", "1980335 5 396067", "396067 7 56581", "56581 7 8083", "8083 59 137", "137 137 1" ]
2122556	2 2 61 8699	[ "2122556 2 1061278", "1061278 2 530639", "530639 61 8699", "8699 8699 1" ]
972077	17 211 271	[ "972077 17 57181", "57181 211 271", "271 271 1" ]
1643145	3 5 7 15649	[ "1643145 3 547715", "547715 5 109543", "109543 7 15649", "15649 15649 1" ]
4601813	367 12539	[ "4601813 367 12539", "12539 12539 1" ]
2599197	3 866399	[ "2599197 3 866399", "866399 866399 1" ]
3576091	3576091	[ "3576091 3576091 1" ]
3274448	2 2 2 2 29 7057	[ "3274448 2 1637224", "1637224 2 818612", "818612 2 409306", "409306 2 204653", "204653 29 7057", "7057 7057 1" ]
267461	17 15733	[ "267461 17 15733", "15733 15733 1" ]
4747966	2 59 40237	[ "4747966 2 2373983", "2373983 59 40237", "40237 40237 1" ]
1680697	1680697	[ "1680697 1680697 1" ]
1557302	2 17 163 281	[ "1557302 2 778651", "778651 17 45803", "45803 163 281", "281 281 1" ]
1281846	2 3 213641	[ "1281846 2 640923", "640923 3 213641", "213641 213641 1" ]
373867	13 28759	[ "373867 13 28759", "28759 28759 1" ]
4581930	2 3 5 163 937	[ "4581930 2 2290965", "2290965 3 763655", "763655 5 152731", "152731 163 937", "937 937 1" ]
4161118	2 13 13 13 947	[ "4161118 2 2080559", "2080559 13 160043", "160043 13 12311", "12311 13 947", "947 947 1" ]
332052	2 2 3 7 59 67	[ "332052 2 166026", "166026 2 83013", "83013 3 27671", "27671 7 3953", "3953 59 67", "67 67 1" ]
3394599	3 13 87041	[ "3394599 3 1131533", "1131533 13 87041", "87041 87041 1" ]
1336583	67 19949	[ "1336583 67 19949", "19949 19949 1" ]
2924513	2924513	[ "2924513 2924513 1" ]
4019387	4019387	[ "4019387 4019387 1" ]
4494542	2 13 172867	[ "4494542 2 2247271", "2247271 13 172867", "172867 172867 1" ]
3925620	2 2 3 3 5 113 193	[ "3925620 2 1962810", "1962810 2 981405", "981405 3 327135", "327135 3 109045", "109045 5 21809", "21809 113 193", "193 193 1" ]
3362623	11 23 13291	[ "3362623 11 305693", "305693 23 13291", "13291 13291 1" ]
2804886	2 3 3 7 113 197	[ "2804886 2 1402443", "1402443 3 467481", "467481 3 155827", "155827 7 22261", "22261 113 197", "197 197 1" ]
2120813	109 19457	[ "2120813 109 19457", "19457 19457 1" ]
603668	2 2 13 13 19 47	[ "603668 2 301834", "301834 2 150917", "150917 13 11609", "11609 13 893", "893 19 47", "47 47 1" ]
3485304	2 2 2 3 3 48407	[ "3485304 2 1742652", "1742652 2 871326", "871326 2 435663", "435663 3 145221", "145221 3 48407", "48407 48407 1" ]
4451848	2 2 2 29 31 619	[ "4451848 2 2225924", "2225924 2 1112962", "1112962 2 556481", "556481 29 19189", "19189 31 619", "619 619 1" ]
2070769	31 67 997	[ "2070769 31 66799", "66799 67 997", "997 997 1" ]
4129978	2 43 48023	[ "4129978 2 2064989", "2064989 43 48023", "48023 48023 1" ]
3601710	2 3 3 5 7 5717	[ "3601710 2 1800855", "1800855 3 600285", "600285 3 200095", "200095 5 40019", "40019 7 5717", "5717 5717 1" ]
2645143	61 103 421	[ "2645143 61 43363", "43363 103 421", "421 421 1" ]
4667724	2 2 3 3 17 29 263	[ "4667724 2 2333862", "2333862 2 1166931", "1166931 3 388977", "388977 3 129659", "129659 17 7627", "7627 29 263", "263 263 1" ]
268632	2 2 2 3 3 7 13 41	[ "268632 2 134316", "134316 2 67158", "67158 2 33579", "33579 3 11193", "11193 3 3731", "3731 7 533", "533 13 41", "41 41 1" ]
3894123	3 43 30187	[ "3894123 3 1298041", "1298041 43 30187", "30187 30187 1" ]
3949612	2 2 41 24083	[ "3949612 2 1974806", "1974806 2 987403", "987403 41 24083", "24083 24083 1" ]
1496188	2 2 374047	[ "1496188 2 748094", "748094 2 374047", "374047 374047 1" ]
1540852	2 2 569 677	[ "1540852 2 770426", "770426 2 385213", "385213 569 677", "677 677 1" ]
1568255	5 13 23 1049	[ "1568255 5 313651", "313651 13 24127", "24127 23 1049", "1049 1049 1" ]
1896014	2 948007	[ "1896014 2 948007", "948007 948007 1" ]
1216011	3 397 1021	[ "1216011 3 405337", "405337 397 1021", "1021 1021 1" ]
598795	5 119759	[ "598795 5 119759", "119759 119759 1" ]
1783175	5 5 71327	[ "1783175 5 356635", "356635 5 71327", "71327 71327 1" ]
3675861	3 3 3 3 3 7 2161	[ "3675861 3 1225287", "1225287 3 408429", "408429 3 136143", "136143 3 45381", "45381 3 15127", "15127 7 2161", "2161 2161 1" ]
4268785	5 17 50221	[ "4268785 5 853757", "853757 17 50221", "50221 50221 1" ]
4287973	4287973	[ "4287973 4287973 1" ]
874555	5 11 15901	[ "874555 5 174911", "174911 11 15901", "15901 15901 1" ]
1280034	2 3 3 7 10159	[ "1280034 2 640017", "640017 3 213339", "213339 3 71113", "71113 7 10159", "10159 10159 1" ]
4779722	2 23 29 3583	[ "4779722 2 2389861", "2389861 23 103907", "103907 29 3583", "3583 3583 1" ]
3461871	3 7 353 467	[ "3461871 3 1153957", "1153957 7 164851", "164851 353 467", "467 467 1" ]
589180	2 2 5 89 331	[ "589180 2 294590", "294590 2 147295", "147295 5 29459", "29459 89 331", "331 331 1" ]
712811	11 11 43 137	[ "712811 11 64801", "64801 11 5891", "5891 43 137", "137 137 1" ]
2881391	2881391	[ "2881391 2881391 1" ]
3301753	7 13 13 2791	[ "3301753 7 471679", "471679 13 36283", "36283 13 2791", "2791 2791 1" ]
4534738	2 13 174413	[ "4534738 2 2267369", "2267369 13 174413", "174413 174413 1" ]
3618766	2 1809383	[ "3618766 2 1809383", "1809383 1809383 1" ]
810220	2 2 5 17 2383	[ "810220 2 405110", "405110 2 202555", "202555 5 40511", "40511 17 2383", "2383 2383 1" ]
4531953	3 1510651	[ "4531953 3 1510651", "1510651 1510651 1" ]
278521	19 107 137	[ "278521 19 14659", "14659 107 137", "137 137 1" ]

1120686

2 3 7 26683

[ "1120686 2 560343", "560343 3 186781", "186781 7 26683", "26683 26683 1" ]

2158306

2 1079153

[ "2158306 2 1079153", "1079153 1079153 1" ]

4233157

419 10103

[ "4233157 419 10103", "10103 10103 1" ]

4564045

5 912809

[ "4564045 5 912809", "912809 912809 1" ]

2050132

2 2 7 17 59 73

[ "2050132 2 1025066", "1025066 2 512533", "512533 7 73219", "73219 17 4307", "4307 59 73", "73 73 1" ]

527062

2 31 8501

[ "527062 2 263531", "263531 31 8501", "8501 8501 1" ]

4999807

191 26177

[ "4999807 191 26177", "26177 26177 1" ]

1265745

3 5 13 6491

[ "1265745 3 421915", "421915 5 84383", "84383 13 6491", "6491 6491 1" ]

3912311

13 257 1171

[ "3912311 13 300947", "300947 257 1171", "1171 1171 1" ]

1861845

3 5 124123

[ "1861845 3 620615", "620615 5 124123", "124123 124123 1" ]

846768

2 2 2 2 3 13 23 59

[ "846768 2 423384", "423384 2 211692", "211692 2 105846", "105846 2 52923", "52923 3 17641", "17641 13 1357", "1357 23 59", "59 59 1" ]

1053717

3 7 50177

[ "1053717 3 351239", "351239 7 50177", "50177 50177 1" ]

1213700

2 2 5 5 53 229

[ "1213700 2 606850", "606850 2 303425", "303425 5 60685", "60685 5 12137", "12137 53 229", "229 229 1" ]

914861

[ "914861 914861 1" ]

4349681

7 7 29 3061

[ "4349681 7 621383", "621383 7 88769", "88769 29 3061", "3061 3061 1" ]

2133335

5 131 3257

[ "2133335 5 426667", "426667 131 3257", "3257 3257 1" ]

2491739

79 31541

[ "2491739 79 31541", "31541 31541 1" ]

227592

2 2 2 3 3 29 109

[ "227592 2 113796", "113796 2 56898", "56898 2 28449", "28449 3 9483", "9483 3 3161", "3161 29 109", "109 109 1" ]

140024

2 2 2 23 761

[ "140024 2 70012", "70012 2 35006", "35006 2 17503", "17503 23 761", "761 761 1" ]

2876786

2 11 43 3041

[ "2876786 2 1438393", "1438393 11 130763", "130763 43 3041", "3041 3041 1" ]

4464379

[ "4464379 4464379 1" ]

256947

3 41 2089

[ "256947 3 85649", "85649 41 2089", "2089 2089 1" ]

1865797

31 139 433

[ "1865797 31 60187", "60187 139 433", "433 433 1" ]

3335596

2 2 11 41 43 43

[ "3335596 2 1667798", "1667798 2 833899", "833899 11 75809", "75809 41 1849", "1849 43 43", "43 43 1" ]

2931000

2 2 2 3 5 5 5 977

[ "2931000 2 1465500", "1465500 2 732750", "732750 2 366375", "366375 3 122125", "122125 5 24425", "24425 5 4885", "4885 5 977", "977 977 1" ]

3126059

71 44029

[ "3126059 71 44029", "44029 44029 1" ]

1016293

199 5107

[ "1016293 199 5107", "5107 5107 1" ]

2138806

2 41 26083

[ "2138806 2 1069403", "1069403 41 26083", "26083 26083 1" ]

4410453

3 1470151

[ "4410453 3 1470151", "1470151 1470151 1" ]

3338182

2 1669091

[ "3338182 2 1669091", "1669091 1669091 1" ]

3945413

[ "3945413 3945413 1" ]

1724999

[ "1724999 1724999 1" ]

2569275

3 3 5 5 19 601

[ "2569275 3 856425", "856425 3 285475", "285475 5 57095", "57095 5 11419", "11419 19 601", "601 601 1" ]

1175999

11 11 9719

[ "1175999 11 106909", "106909 11 9719", "9719 9719 1" ]

1060724

2 2 7 43 881

[ "1060724 2 530362", "530362 2 265181", "265181 7 37883", "37883 43 881", "881 881 1" ]

1736101

[ "1736101 1736101 1" ]

1731933

3 3 7 37 743

[ "1731933 3 577311", "577311 3 192437", "192437 7 27491", "27491 37 743", "743 743 1" ]

3234139

109 29671

[ "3234139 109 29671", "29671 29671 1" ]

395402

2 7 61 463

[ "395402 2 197701", "197701 7 28243", "28243 61 463", "463 463 1" ]

1370339

827 1657

[ "1370339 827 1657", "1657 1657 1" ]

3960670

2 5 7 7 59 137

[ "3960670 2 1980335", "1980335 5 396067", "396067 7 56581", "56581 7 8083", "8083 59 137", "137 137 1" ]

2122556

2 2 61 8699

[ "2122556 2 1061278", "1061278 2 530639", "530639 61 8699", "8699 8699 1" ]

972077

17 211 271

[ "972077 17 57181", "57181 211 271", "271 271 1" ]

1643145

3 5 7 15649

[ "1643145 3 547715", "547715 5 109543", "109543 7 15649", "15649 15649 1" ]

4601813

367 12539

[ "4601813 367 12539", "12539 12539 1" ]

2599197

3 866399

[ "2599197 3 866399", "866399 866399 1" ]

3576091

[ "3576091 3576091 1" ]

3274448

2 2 2 2 29 7057

[ "3274448 2 1637224", "1637224 2 818612", "818612 2 409306", "409306 2 204653", "204653 29 7057", "7057 7057 1" ]

267461

17 15733

[ "267461 17 15733", "15733 15733 1" ]

4747966

2 59 40237

[ "4747966 2 2373983", "2373983 59 40237", "40237 40237 1" ]

1680697

[ "1680697 1680697 1" ]

1557302

2 17 163 281

[ "1557302 2 778651", "778651 17 45803", "45803 163 281", "281 281 1" ]

1281846

2 3 213641

[ "1281846 2 640923", "640923 3 213641", "213641 213641 1" ]

373867

13 28759

[ "373867 13 28759", "28759 28759 1" ]

4581930

2 3 5 163 937

[ "4581930 2 2290965", "2290965 3 763655", "763655 5 152731", "152731 163 937", "937 937 1" ]

4161118

2 13 13 13 947

[ "4161118 2 2080559", "2080559 13 160043", "160043 13 12311", "12311 13 947", "947 947 1" ]

332052

2 2 3 7 59 67

[ "332052 2 166026", "166026 2 83013", "83013 3 27671", "27671 7 3953", "3953 59 67", "67 67 1" ]

3394599

3 13 87041

[ "3394599 3 1131533", "1131533 13 87041", "87041 87041 1" ]

1336583

67 19949

[ "1336583 67 19949", "19949 19949 1" ]

2924513

[ "2924513 2924513 1" ]

4019387

[ "4019387 4019387 1" ]

4494542

2 13 172867

[ "4494542 2 2247271", "2247271 13 172867", "172867 172867 1" ]

3925620

2 2 3 3 5 113 193

[ "3925620 2 1962810", "1962810 2 981405", "981405 3 327135", "327135 3 109045", "109045 5 21809", "21809 113 193", "193 193 1" ]

3362623

11 23 13291

[ "3362623 11 305693", "305693 23 13291", "13291 13291 1" ]

2804886

2 3 3 7 113 197

[ "2804886 2 1402443", "1402443 3 467481", "467481 3 155827", "155827 7 22261", "22261 113 197", "197 197 1" ]

2120813

109 19457

[ "2120813 109 19457", "19457 19457 1" ]

603668

2 2 13 13 19 47

[ "603668 2 301834", "301834 2 150917", "150917 13 11609", "11609 13 893", "893 19 47", "47 47 1" ]

3485304

2 2 2 3 3 48407

[ "3485304 2 1742652", "1742652 2 871326", "871326 2 435663", "435663 3 145221", "145221 3 48407", "48407 48407 1" ]

4451848

2 2 2 29 31 619

[ "4451848 2 2225924", "2225924 2 1112962", "1112962 2 556481", "556481 29 19189", "19189 31 619", "619 619 1" ]

2070769

31 67 997

[ "2070769 31 66799", "66799 67 997", "997 997 1" ]

4129978

2 43 48023

[ "4129978 2 2064989", "2064989 43 48023", "48023 48023 1" ]

3601710

2 3 3 5 7 5717

[ "3601710 2 1800855", "1800855 3 600285", "600285 3 200095", "200095 5 40019", "40019 7 5717", "5717 5717 1" ]

2645143

61 103 421

[ "2645143 61 43363", "43363 103 421", "421 421 1" ]

4667724

2 2 3 3 17 29 263

[ "4667724 2 2333862", "2333862 2 1166931", "1166931 3 388977", "388977 3 129659", "129659 17 7627", "7627 29 263", "263 263 1" ]

268632

2 2 2 3 3 7 13 41

[ "268632 2 134316", "134316 2 67158", "67158 2 33579", "33579 3 11193", "11193 3 3731", "3731 7 533", "533 13 41", "41 41 1" ]

3894123

3 43 30187

[ "3894123 3 1298041", "1298041 43 30187", "30187 30187 1" ]

3949612

2 2 41 24083

[ "3949612 2 1974806", "1974806 2 987403", "987403 41 24083", "24083 24083 1" ]

1496188

2 2 374047

[ "1496188 2 748094", "748094 2 374047", "374047 374047 1" ]

1540852

2 2 569 677

[ "1540852 2 770426", "770426 2 385213", "385213 569 677", "677 677 1" ]

1568255

5 13 23 1049

[ "1568255 5 313651", "313651 13 24127", "24127 23 1049", "1049 1049 1" ]

1896014

2 948007

[ "1896014 2 948007", "948007 948007 1" ]

1216011

3 397 1021

[ "1216011 3 405337", "405337 397 1021", "1021 1021 1" ]

598795

5 119759

[ "598795 5 119759", "119759 119759 1" ]

1783175

5 5 71327

[ "1783175 5 356635", "356635 5 71327", "71327 71327 1" ]

3675861

3 3 3 3 3 7 2161

[ "3675861 3 1225287", "1225287 3 408429", "408429 3 136143", "136143 3 45381", "45381 3 15127", "15127 7 2161", "2161 2161 1" ]

4268785

5 17 50221

[ "4268785 5 853757", "853757 17 50221", "50221 50221 1" ]

4287973

[ "4287973 4287973 1" ]

874555

5 11 15901

[ "874555 5 174911", "174911 11 15901", "15901 15901 1" ]

1280034

2 3 3 7 10159

[ "1280034 2 640017", "640017 3 213339", "213339 3 71113", "71113 7 10159", "10159 10159 1" ]

4779722

2 23 29 3583

[ "4779722 2 2389861", "2389861 23 103907", "103907 29 3583", "3583 3583 1" ]

3461871

3 7 353 467

[ "3461871 3 1153957", "1153957 7 164851", "164851 353 467", "467 467 1" ]

589180

2 2 5 89 331

[ "589180 2 294590", "294590 2 147295", "147295 5 29459", "29459 89 331", "331 331 1" ]

712811

11 11 43 137

[ "712811 11 64801", "64801 11 5891", "5891 43 137", "137 137 1" ]

2881391

[ "2881391 2881391 1" ]

3301753

7 13 13 2791

[ "3301753 7 471679", "471679 13 36283", "36283 13 2791", "2791 2791 1" ]

4534738

2 13 174413

[ "4534738 2 2267369", "2267369 13 174413", "174413 174413 1" ]

3618766

2 1809383

[ "3618766 2 1809383", "1809383 1809383 1" ]

810220

2 2 5 17 2383

[ "810220 2 405110", "405110 2 202555", "202555 5 40511", "40511 17 2383", "2383 2383 1" ]

4531953

3 1510651

[ "4531953 3 1510651", "1510651 1510651 1" ]

278521

19 107 137

[ "278521 19 14659", "14659 107 137", "137 137 1" ]