yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
2867081	7 19 21557	[ "2867081 7 409583", "409583 19 21557", "21557 21557 1" ]
1049074	2 13 157 257	[ "1049074 2 524537", "524537 13 40349", "40349 157 257", "257 257 1" ]
2963120	2 2 2 2 5 37039	[ "2963120 2 1481560", "1481560 2 740780", "740780 2 370390", "370390 2 185195", "185195 5 37039", "37039 37039 1" ]
1179051	3 393017	[ "1179051 3 393017", "393017 393017 1" ]
4706073	3 3 3 174299	[ "4706073 3 1568691", "1568691 3 522897", "522897 3 174299", "174299 174299 1" ]
4630682	2 7 23 73 197	[ "4630682 2 2315341", "2315341 7 330763", "330763 23 14381", "14381 73 197", "197 197 1" ]
3846705	3 5 29 37 239	[ "3846705 3 1282235", "1282235 5 256447", "256447 29 8843", "8843 37 239", "239 239 1" ]
1967388	2 2 3 67 2447	[ "1967388 2 983694", "983694 2 491847", "491847 3 163949", "163949 67 2447", "2447 2447 1" ]
2062922	2 1031461	[ "2062922 2 1031461", "1031461 1031461 1" ]
3141712	2 2 2 2 7 28051	[ "3141712 2 1570856", "1570856 2 785428", "785428 2 392714", "392714 2 196357", "196357 7 28051", "28051 28051 1" ]
1979006	2 151 6553	[ "1979006 2 989503", "989503 151 6553", "6553 6553 1" ]
2393878	2 1196939	[ "2393878 2 1196939", "1196939 1196939 1" ]
4078444	2 2 29 35159	[ "4078444 2 2039222", "2039222 2 1019611", "1019611 29 35159", "35159 35159 1" ]
1872107	127 14741	[ "1872107 127 14741", "14741 14741 1" ]
2874132	2 2 3 3 29 2753	[ "2874132 2 1437066", "1437066 2 718533", "718533 3 239511", "239511 3 79837", "79837 29 2753", "2753 2753 1" ]
108002	2 54001	[ "108002 2 54001", "54001 54001 1" ]
95912	2 2 2 19 631	[ "95912 2 47956", "47956 2 23978", "23978 2 11989", "11989 19 631", "631 631 1" ]
4426216	2 2 2 553277	[ "4426216 2 2213108", "2213108 2 1106554", "1106554 2 553277", "553277 553277 1" ]
3790995	3 5 13 19441	[ "3790995 3 1263665", "1263665 5 252733", "252733 13 19441", "19441 19441 1" ]
577918	2 11 109 241	[ "577918 2 288959", "288959 11 26269", "26269 109 241", "241 241 1" ]
4264424	2 2 2 533053	[ "4264424 2 2132212", "2132212 2 1066106", "1066106 2 533053", "533053 533053 1" ]
4740925	5 5 7 27091	[ "4740925 5 948185", "948185 5 189637", "189637 7 27091", "27091 27091 1" ]
4955690	2 5 495569	[ "4955690 2 2477845", "2477845 5 495569", "495569 495569 1" ]
2279793	3 131 5801	[ "2279793 3 759931", "759931 131 5801", "5801 5801 1" ]
3155848	2 2 2 394481	[ "3155848 2 1577924", "1577924 2 788962", "788962 2 394481", "394481 394481 1" ]
1502444	2 2 19 53 373	[ "1502444 2 751222", "751222 2 375611", "375611 19 19769", "19769 53 373", "373 373 1" ]
4563286	2 7 13 25073	[ "4563286 2 2281643", "2281643 7 325949", "325949 13 25073", "25073 25073 1" ]
1348132	2 2 37 9109	[ "1348132 2 674066", "674066 2 337033", "337033 37 9109", "9109 9109 1" ]
4723541	409 11549	[ "4723541 409 11549", "11549 11549 1" ]
1473782	2 43 17137	[ "1473782 2 736891", "736891 43 17137", "17137 17137 1" ]
4685162	2 37 63313	[ "4685162 2 2342581", "2342581 37 63313", "63313 63313 1" ]
2561793	3 13 65687	[ "2561793 3 853931", "853931 13 65687", "65687 65687 1" ]
3969962	2 1984981	[ "3969962 2 1984981", "1984981 1984981 1" ]
3921976	2 2 2 490247	[ "3921976 2 1960988", "1960988 2 980494", "980494 2 490247", "490247 490247 1" ]
2688308	2 2 7 67 1433	[ "2688308 2 1344154", "1344154 2 672077", "672077 7 96011", "96011 67 1433", "1433 1433 1" ]
4449268	2 2 19 58543	[ "4449268 2 2224634", "2224634 2 1112317", "1112317 19 58543", "58543 58543 1" ]
3435073	23 149351	[ "3435073 23 149351", "149351 149351 1" ]
4668947	4668947	[ "4668947 4668947 1" ]
4162495	5 832499	[ "4162495 5 832499", "832499 832499 1" ]
253196	2 2 63299	[ "253196 2 126598", "126598 2 63299", "63299 63299 1" ]
861321	3 287107	[ "861321 3 287107", "287107 287107 1" ]
1994336	2 2 2 2 2 62323	[ "1994336 2 997168", "997168 2 498584", "498584 2 249292", "249292 2 124646", "124646 2 62323", "62323 62323 1" ]
1530380	2 2 5 76519	[ "1530380 2 765190", "765190 2 382595", "382595 5 76519", "76519 76519 1" ]
2807353	2807353	[ "2807353 2807353 1" ]
4711367	4711367	[ "4711367 4711367 1" ]
309306	2 3 51551	[ "309306 2 154653", "154653 3 51551", "51551 51551 1" ]
2587113	3 3 3 95819	[ "2587113 3 862371", "862371 3 287457", "287457 3 95819", "95819 95819 1" ]
2777795	5 431 1289	[ "2777795 5 555559", "555559 431 1289", "1289 1289 1" ]
3015191	47 64153	[ "3015191 47 64153", "64153 64153 1" ]
482311	73 6607	[ "482311 73 6607", "6607 6607 1" ]
1497638	2 748819	[ "1497638 2 748819", "748819 748819 1" ]
2091549	3 197 3539	[ "2091549 3 697183", "697183 197 3539", "3539 3539 1" ]
1795233	3 11 54401	[ "1795233 3 598411", "598411 11 54401", "54401 54401 1" ]
2221186	2 11 17 5939	[ "2221186 2 1110593", "1110593 11 100963", "100963 17 5939", "5939 5939 1" ]
4882558	2 67 83 439	[ "4882558 2 2441279", "2441279 67 36437", "36437 83 439", "439 439 1" ]
1444498	2 11 11 47 127	[ "1444498 2 722249", "722249 11 65659", "65659 11 5969", "5969 47 127", "127 127 1" ]
274761	3 3 30529	[ "274761 3 91587", "91587 3 30529", "30529 30529 1" ]
3733684	2 2 933421	[ "3733684 2 1866842", "1866842 2 933421", "933421 933421 1" ]
1719877	1719877	[ "1719877 1719877 1" ]
1604961	3 3 3 59443	[ "1604961 3 534987", "534987 3 178329", "178329 3 59443", "59443 59443 1" ]
2230482	2 3 41 9067	[ "2230482 2 1115241", "1115241 3 371747", "371747 41 9067", "9067 9067 1" ]
939560	2 2 2 5 83 283	[ "939560 2 469780", "469780 2 234890", "234890 2 117445", "117445 5 23489", "23489 83 283", "283 283 1" ]
2723380	2 2 5 11 12379	[ "2723380 2 1361690", "1361690 2 680845", "680845 5 136169", "136169 11 12379", "12379 12379 1" ]
527122	2 263561	[ "527122 2 263561", "263561 263561 1" ]
3642269	3642269	[ "3642269 3642269 1" ]
3314057	787 4211	[ "3314057 787 4211", "4211 4211 1" ]
3141213	3 19 55109	[ "3141213 3 1047071", "1047071 19 55109", "55109 55109 1" ]
2517410	2 5 7 35963	[ "2517410 2 1258705", "1258705 5 251741", "251741 7 35963", "35963 35963 1" ]
3924384	2 2 2 2 2 3 40879	[ "3924384 2 1962192", "1962192 2 981096", "981096 2 490548", "490548 2 245274", "245274 2 122637", "122637 3 40879", "40879 40879 1" ]
2615422	2 23 56857	[ "2615422 2 1307711", "1307711 23 56857", "56857 56857 1" ]
1633906	2 269 3037	[ "1633906 2 816953", "816953 269 3037", "3037 3037 1" ]
3465778	2 23 59 1277	[ "3465778 2 1732889", "1732889 23 75343", "75343 59 1277", "1277 1277 1" ]
1740956	2 2 7 97 641	[ "1740956 2 870478", "870478 2 435239", "435239 7 62177", "62177 97 641", "641 641 1" ]
2669330	2 5 266933	[ "2669330 2 1334665", "1334665 5 266933", "266933 266933 1" ]
4487116	2 2 17 19 23 151	[ "4487116 2 2243558", "2243558 2 1121779", "1121779 17 65987", "65987 19 3473", "3473 23 151", "151 151 1" ]
1818753	3 606251	[ "1818753 3 606251", "606251 606251 1" ]
830777	830777	[ "830777 830777 1" ]
1561273	7 29 7691	[ "1561273 7 223039", "223039 29 7691", "7691 7691 1" ]
1281000	2 2 2 3 5 5 5 7 61	[ "1281000 2 640500", "640500 2 320250", "320250 2 160125", "160125 3 53375", "53375 5 10675", "10675 5 2135", "2135 5 427", "427 7 61", "61 61 1" ]
2217708	2 2 3 3 61603	[ "2217708 2 1108854", "1108854 2 554427", "554427 3 184809", "184809 3 61603", "61603 61603 1" ]
4531675	5 5 109 1663	[ "4531675 5 906335", "906335 5 181267", "181267 109 1663", "1663 1663 1" ]
723280	2 2 2 2 5 9041	[ "723280 2 361640", "361640 2 180820", "180820 2 90410", "90410 2 45205", "45205 5 9041", "9041 9041 1" ]
4963730	2 5 107 4639	[ "4963730 2 2481865", "2481865 5 496373", "496373 107 4639", "4639 4639 1" ]
4393669	7 627667	[ "4393669 7 627667", "627667 627667 1" ]
1901747	59 32233	[ "1901747 59 32233", "32233 32233 1" ]
4468461	3 383 3889	[ "4468461 3 1489487", "1489487 383 3889", "3889 3889 1" ]
2530702	2 179 7069	[ "2530702 2 1265351", "1265351 179 7069", "7069 7069 1" ]
3754333	11 341303	[ "3754333 11 341303", "341303 341303 1" ]
2538966	2 3 41 10321	[ "2538966 2 1269483", "1269483 3 423161", "423161 41 10321", "10321 10321 1" ]
398133	3 3 31 1427	[ "398133 3 132711", "132711 3 44237", "44237 31 1427", "1427 1427 1" ]
3180955	5 17 37423	[ "3180955 5 636191", "636191 17 37423", "37423 37423 1" ]
923493	3 307831	[ "923493 3 307831", "307831 307831 1" ]
3872808	2 2 2 3 3 19 19 149	[ "3872808 2 1936404", "1936404 2 968202", "968202 2 484101", "484101 3 161367", "161367 3 53789", "53789 19 2831", "2831 19 149", "149 149 1" ]
934107	3 103 3023	[ "934107 3 311369", "311369 103 3023", "3023 3023 1" ]
1038969	3 3 67 1723	[ "1038969 3 346323", "346323 3 115441", "115441 67 1723", "1723 1723 1" ]
2078591	2078591	[ "2078591 2078591 1" ]
4749827	4749827	[ "4749827 4749827 1" ]
130159	73 1783	[ "130159 73 1783", "1783 1783 1" ]
2269881	3 3 252209	[ "2269881 3 756627", "756627 3 252209", "252209 252209 1" ]
4210682	2 7 67 67 67	[ "4210682 2 2105341", "2105341 7 300763", "300763 67 4489", "4489 67 67", "67 67 1" ]

2867081

7 19 21557

[ "2867081 7 409583", "409583 19 21557", "21557 21557 1" ]

1049074

2 13 157 257

[ "1049074 2 524537", "524537 13 40349", "40349 157 257", "257 257 1" ]

2963120

2 2 2 2 5 37039

[ "2963120 2 1481560", "1481560 2 740780", "740780 2 370390", "370390 2 185195", "185195 5 37039", "37039 37039 1" ]

1179051

3 393017

[ "1179051 3 393017", "393017 393017 1" ]

4706073

3 3 3 174299

[ "4706073 3 1568691", "1568691 3 522897", "522897 3 174299", "174299 174299 1" ]

4630682

2 7 23 73 197

[ "4630682 2 2315341", "2315341 7 330763", "330763 23 14381", "14381 73 197", "197 197 1" ]

3846705

3 5 29 37 239

[ "3846705 3 1282235", "1282235 5 256447", "256447 29 8843", "8843 37 239", "239 239 1" ]

1967388

2 2 3 67 2447

[ "1967388 2 983694", "983694 2 491847", "491847 3 163949", "163949 67 2447", "2447 2447 1" ]

2062922

2 1031461

[ "2062922 2 1031461", "1031461 1031461 1" ]

3141712

2 2 2 2 7 28051

[ "3141712 2 1570856", "1570856 2 785428", "785428 2 392714", "392714 2 196357", "196357 7 28051", "28051 28051 1" ]

1979006

2 151 6553

[ "1979006 2 989503", "989503 151 6553", "6553 6553 1" ]

2393878

2 1196939

[ "2393878 2 1196939", "1196939 1196939 1" ]

4078444

2 2 29 35159

[ "4078444 2 2039222", "2039222 2 1019611", "1019611 29 35159", "35159 35159 1" ]

1872107

127 14741

[ "1872107 127 14741", "14741 14741 1" ]

2874132

2 2 3 3 29 2753

[ "2874132 2 1437066", "1437066 2 718533", "718533 3 239511", "239511 3 79837", "79837 29 2753", "2753 2753 1" ]

108002

2 54001

[ "108002 2 54001", "54001 54001 1" ]

95912

2 2 2 19 631

[ "95912 2 47956", "47956 2 23978", "23978 2 11989", "11989 19 631", "631 631 1" ]

4426216

2 2 2 553277

[ "4426216 2 2213108", "2213108 2 1106554", "1106554 2 553277", "553277 553277 1" ]

3790995

3 5 13 19441

[ "3790995 3 1263665", "1263665 5 252733", "252733 13 19441", "19441 19441 1" ]

577918

2 11 109 241

[ "577918 2 288959", "288959 11 26269", "26269 109 241", "241 241 1" ]

4264424

2 2 2 533053

[ "4264424 2 2132212", "2132212 2 1066106", "1066106 2 533053", "533053 533053 1" ]

4740925

5 5 7 27091

[ "4740925 5 948185", "948185 5 189637", "189637 7 27091", "27091 27091 1" ]

4955690

2 5 495569

[ "4955690 2 2477845", "2477845 5 495569", "495569 495569 1" ]

2279793

3 131 5801

[ "2279793 3 759931", "759931 131 5801", "5801 5801 1" ]

3155848

2 2 2 394481

[ "3155848 2 1577924", "1577924 2 788962", "788962 2 394481", "394481 394481 1" ]

1502444

2 2 19 53 373

[ "1502444 2 751222", "751222 2 375611", "375611 19 19769", "19769 53 373", "373 373 1" ]

4563286

2 7 13 25073

[ "4563286 2 2281643", "2281643 7 325949", "325949 13 25073", "25073 25073 1" ]

1348132

2 2 37 9109

[ "1348132 2 674066", "674066 2 337033", "337033 37 9109", "9109 9109 1" ]

4723541

409 11549

[ "4723541 409 11549", "11549 11549 1" ]

1473782

2 43 17137

[ "1473782 2 736891", "736891 43 17137", "17137 17137 1" ]

4685162

2 37 63313

[ "4685162 2 2342581", "2342581 37 63313", "63313 63313 1" ]

2561793

3 13 65687

[ "2561793 3 853931", "853931 13 65687", "65687 65687 1" ]

3969962

2 1984981

[ "3969962 2 1984981", "1984981 1984981 1" ]

3921976

2 2 2 490247

[ "3921976 2 1960988", "1960988 2 980494", "980494 2 490247", "490247 490247 1" ]

2688308

2 2 7 67 1433

[ "2688308 2 1344154", "1344154 2 672077", "672077 7 96011", "96011 67 1433", "1433 1433 1" ]

4449268

2 2 19 58543

[ "4449268 2 2224634", "2224634 2 1112317", "1112317 19 58543", "58543 58543 1" ]

3435073

23 149351

[ "3435073 23 149351", "149351 149351 1" ]

4668947

[ "4668947 4668947 1" ]

4162495

5 832499

[ "4162495 5 832499", "832499 832499 1" ]

253196

2 2 63299

[ "253196 2 126598", "126598 2 63299", "63299 63299 1" ]

861321

3 287107

[ "861321 3 287107", "287107 287107 1" ]

1994336

2 2 2 2 2 62323

[ "1994336 2 997168", "997168 2 498584", "498584 2 249292", "249292 2 124646", "124646 2 62323", "62323 62323 1" ]

1530380

2 2 5 76519

[ "1530380 2 765190", "765190 2 382595", "382595 5 76519", "76519 76519 1" ]

2807353

[ "2807353 2807353 1" ]

4711367

[ "4711367 4711367 1" ]

309306

2 3 51551

[ "309306 2 154653", "154653 3 51551", "51551 51551 1" ]

2587113

3 3 3 95819

[ "2587113 3 862371", "862371 3 287457", "287457 3 95819", "95819 95819 1" ]

2777795

5 431 1289

[ "2777795 5 555559", "555559 431 1289", "1289 1289 1" ]

3015191

47 64153

[ "3015191 47 64153", "64153 64153 1" ]

482311

73 6607

[ "482311 73 6607", "6607 6607 1" ]

1497638

2 748819

[ "1497638 2 748819", "748819 748819 1" ]

2091549

3 197 3539

[ "2091549 3 697183", "697183 197 3539", "3539 3539 1" ]

1795233

3 11 54401

[ "1795233 3 598411", "598411 11 54401", "54401 54401 1" ]

2221186

2 11 17 5939

[ "2221186 2 1110593", "1110593 11 100963", "100963 17 5939", "5939 5939 1" ]

4882558

2 67 83 439

[ "4882558 2 2441279", "2441279 67 36437", "36437 83 439", "439 439 1" ]

1444498

2 11 11 47 127

[ "1444498 2 722249", "722249 11 65659", "65659 11 5969", "5969 47 127", "127 127 1" ]

274761

3 3 30529

[ "274761 3 91587", "91587 3 30529", "30529 30529 1" ]

3733684

2 2 933421

[ "3733684 2 1866842", "1866842 2 933421", "933421 933421 1" ]

1719877

[ "1719877 1719877 1" ]

1604961

3 3 3 59443

[ "1604961 3 534987", "534987 3 178329", "178329 3 59443", "59443 59443 1" ]

2230482

2 3 41 9067

[ "2230482 2 1115241", "1115241 3 371747", "371747 41 9067", "9067 9067 1" ]

939560

2 2 2 5 83 283

[ "939560 2 469780", "469780 2 234890", "234890 2 117445", "117445 5 23489", "23489 83 283", "283 283 1" ]

2723380

2 2 5 11 12379

[ "2723380 2 1361690", "1361690 2 680845", "680845 5 136169", "136169 11 12379", "12379 12379 1" ]

527122

2 263561

[ "527122 2 263561", "263561 263561 1" ]

3642269

[ "3642269 3642269 1" ]

3314057

787 4211

[ "3314057 787 4211", "4211 4211 1" ]

3141213

3 19 55109

[ "3141213 3 1047071", "1047071 19 55109", "55109 55109 1" ]

2517410

2 5 7 35963

[ "2517410 2 1258705", "1258705 5 251741", "251741 7 35963", "35963 35963 1" ]

3924384

2 2 2 2 2 3 40879

[ "3924384 2 1962192", "1962192 2 981096", "981096 2 490548", "490548 2 245274", "245274 2 122637", "122637 3 40879", "40879 40879 1" ]

2615422

2 23 56857

[ "2615422 2 1307711", "1307711 23 56857", "56857 56857 1" ]

1633906

2 269 3037

[ "1633906 2 816953", "816953 269 3037", "3037 3037 1" ]

3465778

2 23 59 1277

[ "3465778 2 1732889", "1732889 23 75343", "75343 59 1277", "1277 1277 1" ]

1740956

2 2 7 97 641

[ "1740956 2 870478", "870478 2 435239", "435239 7 62177", "62177 97 641", "641 641 1" ]

2669330

2 5 266933

[ "2669330 2 1334665", "1334665 5 266933", "266933 266933 1" ]

4487116

2 2 17 19 23 151

[ "4487116 2 2243558", "2243558 2 1121779", "1121779 17 65987", "65987 19 3473", "3473 23 151", "151 151 1" ]

1818753

3 606251

[ "1818753 3 606251", "606251 606251 1" ]

830777

[ "830777 830777 1" ]

1561273

7 29 7691

[ "1561273 7 223039", "223039 29 7691", "7691 7691 1" ]

1281000

2 2 2 3 5 5 5 7 61

[ "1281000 2 640500", "640500 2 320250", "320250 2 160125", "160125 3 53375", "53375 5 10675", "10675 5 2135", "2135 5 427", "427 7 61", "61 61 1" ]

2217708

2 2 3 3 61603

[ "2217708 2 1108854", "1108854 2 554427", "554427 3 184809", "184809 3 61603", "61603 61603 1" ]

4531675

5 5 109 1663

[ "4531675 5 906335", "906335 5 181267", "181267 109 1663", "1663 1663 1" ]

723280

2 2 2 2 5 9041

[ "723280 2 361640", "361640 2 180820", "180820 2 90410", "90410 2 45205", "45205 5 9041", "9041 9041 1" ]

4963730

2 5 107 4639

[ "4963730 2 2481865", "2481865 5 496373", "496373 107 4639", "4639 4639 1" ]

4393669

7 627667

[ "4393669 7 627667", "627667 627667 1" ]

1901747

59 32233

[ "1901747 59 32233", "32233 32233 1" ]

4468461

3 383 3889

[ "4468461 3 1489487", "1489487 383 3889", "3889 3889 1" ]

2530702

2 179 7069

[ "2530702 2 1265351", "1265351 179 7069", "7069 7069 1" ]

3754333

11 341303

[ "3754333 11 341303", "341303 341303 1" ]

2538966

2 3 41 10321

[ "2538966 2 1269483", "1269483 3 423161", "423161 41 10321", "10321 10321 1" ]

398133

3 3 31 1427

[ "398133 3 132711", "132711 3 44237", "44237 31 1427", "1427 1427 1" ]

3180955

5 17 37423

[ "3180955 5 636191", "636191 17 37423", "37423 37423 1" ]

923493

3 307831

[ "923493 3 307831", "307831 307831 1" ]

3872808

2 2 2 3 3 19 19 149

[ "3872808 2 1936404", "1936404 2 968202", "968202 2 484101", "484101 3 161367", "161367 3 53789", "53789 19 2831", "2831 19 149", "149 149 1" ]

934107

3 103 3023

[ "934107 3 311369", "311369 103 3023", "3023 3023 1" ]

1038969

3 3 67 1723

[ "1038969 3 346323", "346323 3 115441", "115441 67 1723", "1723 1723 1" ]

2078591

[ "2078591 2078591 1" ]

4749827

[ "4749827 4749827 1" ]

130159

73 1783

[ "130159 73 1783", "1783 1783 1" ]

2269881

3 3 252209

[ "2269881 3 756627", "756627 3 252209", "252209 252209 1" ]

4210682

2 7 67 67 67

[ "4210682 2 2105341", "2105341 7 300763", "300763 67 4489", "4489 67 67", "67 67 1" ]