yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
1772115	3 5 31 37 103	[ "1772115 3 590705", "590705 5 118141", "118141 31 3811", "3811 37 103", "103 103 1" ]
3371868	2 2 3 3 3 3 3 3469	[ "3371868 2 1685934", "1685934 2 842967", "842967 3 280989", "280989 3 93663", "93663 3 31221", "31221 3 10407", "10407 3 3469", "3469 3469 1" ]
2212446	2 3 491 751	[ "2212446 2 1106223", "1106223 3 368741", "368741 491 751", "751 751 1" ]
2033276	2 2 7 72617	[ "2033276 2 1016638", "1016638 2 508319", "508319 7 72617", "72617 72617 1" ]
3735173	13 287321	[ "3735173 13 287321", "287321 287321 1" ]
3176296	2 2 2 397037	[ "3176296 2 1588148", "1588148 2 794074", "794074 2 397037", "397037 397037 1" ]
62771	41 1531	[ "62771 41 1531", "1531 1531 1" ]
3229607	239 13513	[ "3229607 239 13513", "13513 13513 1" ]
353069	353069	[ "353069 353069 1" ]
1978133	401 4933	[ "1978133 401 4933", "4933 4933 1" ]
354277	7 11 43 107	[ "354277 7 50611", "50611 11 4601", "4601 43 107", "107 107 1" ]
3449362	2 7 37 6659	[ "3449362 2 1724681", "1724681 7 246383", "246383 37 6659", "6659 6659 1" ]
4245349	461 9209	[ "4245349 461 9209", "9209 9209 1" ]
2747575	5 5 109903	[ "2747575 5 549515", "549515 5 109903", "109903 109903 1" ]
3156807	3 1052269	[ "3156807 3 1052269", "1052269 1052269 1" ]
4588356	2 2 3 382363	[ "4588356 2 2294178", "2294178 2 1147089", "1147089 3 382363", "382363 382363 1" ]
4979327	41 121447	[ "4979327 41 121447", "121447 121447 1" ]
3362234	2 73 23029	[ "3362234 2 1681117", "1681117 73 23029", "23029 23029 1" ]
2492489	17 146617	[ "2492489 17 146617", "146617 146617 1" ]
3623339	61 59399	[ "3623339 61 59399", "59399 59399 1" ]
3406380	2 2 3 5 56773	[ "3406380 2 1703190", "1703190 2 851595", "851595 3 283865", "283865 5 56773", "56773 56773 1" ]
2987836	2 2 746959	[ "2987836 2 1493918", "1493918 2 746959", "746959 746959 1" ]
3475880	2 2 2 5 113 769	[ "3475880 2 1737940", "1737940 2 868970", "868970 2 434485", "434485 5 86897", "86897 113 769", "769 769 1" ]
2692716	2 2 3 13 41 421	[ "2692716 2 1346358", "1346358 2 673179", "673179 3 224393", "224393 13 17261", "17261 41 421", "421 421 1" ]
3768808	2 2 2 471101	[ "3768808 2 1884404", "1884404 2 942202", "942202 2 471101", "471101 471101 1" ]
4586166	2 3 3 3 13 47 139	[ "4586166 2 2293083", "2293083 3 764361", "764361 3 254787", "254787 3 84929", "84929 13 6533", "6533 47 139", "139 139 1" ]
1362619	1362619	[ "1362619 1362619 1" ]
1888567	29 65123	[ "1888567 29 65123", "65123 65123 1" ]
3276875	5 5 5 5 7 7 107	[ "3276875 5 655375", "655375 5 131075", "131075 5 26215", "26215 5 5243", "5243 7 749", "749 7 107", "107 107 1" ]
4619382	2 3 67 11491	[ "4619382 2 2309691", "2309691 3 769897", "769897 67 11491", "11491 11491 1" ]
1554384	2 2 2 2 3 13 47 53	[ "1554384 2 777192", "777192 2 388596", "388596 2 194298", "194298 2 97149", "97149 3 32383", "32383 13 2491", "2491 47 53", "53 53 1" ]
3205522	2 1602761	[ "3205522 2 1602761", "1602761 1602761 1" ]
3561139	37 109 883	[ "3561139 37 96247", "96247 109 883", "883 883 1" ]
2244850	2 5 5 17 19 139	[ "2244850 2 1122425", "1122425 5 224485", "224485 5 44897", "44897 17 2641", "2641 19 139", "139 139 1" ]
1231564	2 2 307891	[ "1231564 2 615782", "615782 2 307891", "307891 307891 1" ]
321243	3 13 8237	[ "321243 3 107081", "107081 13 8237", "8237 8237 1" ]
2487951	3 3 276439	[ "2487951 3 829317", "829317 3 276439", "276439 276439 1" ]
3409255	5 43 101 157	[ "3409255 5 681851", "681851 43 15857", "15857 101 157", "157 157 1" ]
230200	2 2 2 5 5 1151	[ "230200 2 115100", "115100 2 57550", "57550 2 28775", "28775 5 5755", "5755 5 1151", "1151 1151 1" ]
322836	2 2 3 26903	[ "322836 2 161418", "161418 2 80709", "80709 3 26903", "26903 26903 1" ]
2499959	7 11 32467	[ "2499959 7 357137", "357137 11 32467", "32467 32467 1" ]
3584017	3584017	[ "3584017 3584017 1" ]
1863579	3 37 103 163	[ "1863579 3 621193", "621193 37 16789", "16789 103 163", "163 163 1" ]
663583	663583	[ "663583 663583 1" ]
531600	2 2 2 2 3 5 5 443	[ "531600 2 265800", "265800 2 132900", "132900 2 66450", "66450 2 33225", "33225 3 11075", "11075 5 2215", "2215 5 443", "443 443 1" ]
1900831	1900831	[ "1900831 1900831 1" ]
2803451	7 619 647	[ "2803451 7 400493", "400493 619 647", "647 647 1" ]
3239328	2 2 2 2 2 3 41 823	[ "3239328 2 1619664", "1619664 2 809832", "809832 2 404916", "404916 2 202458", "202458 2 101229", "101229 3 33743", "33743 41 823", "823 823 1" ]
1628052	2 2 3 135671	[ "1628052 2 814026", "814026 2 407013", "407013 3 135671", "135671 135671 1" ]
1171593	3 3 349 373	[ "1171593 3 390531", "390531 3 130177", "130177 349 373", "373 373 1" ]
585287	197 2971	[ "585287 197 2971", "2971 2971 1" ]
4240846	2 2120423	[ "4240846 2 2120423", "2120423 2120423 1" ]
2341879	41 57119	[ "2341879 41 57119", "57119 57119 1" ]
4844935	5 571 1697	[ "4844935 5 968987", "968987 571 1697", "1697 1697 1" ]
409609	409609	[ "409609 409609 1" ]
4591765	5 918353	[ "4591765 5 918353", "918353 918353 1" ]
490290	2 3 5 59 277	[ "490290 2 245145", "245145 3 81715", "81715 5 16343", "16343 59 277", "277 277 1" ]
2062453	79 26107	[ "2062453 79 26107", "26107 26107 1" ]
2079731	83 25057	[ "2079731 83 25057", "25057 25057 1" ]
2712773	7 191 2029	[ "2712773 7 387539", "387539 191 2029", "2029 2029 1" ]
169664	2 2 2 2 2 2 11 241	[ "169664 2 84832", "84832 2 42416", "42416 2 21208", "21208 2 10604", "10604 2 5302", "5302 2 2651", "2651 11 241", "241 241 1" ]
266356	2 2 17 3917	[ "266356 2 133178", "133178 2 66589", "66589 17 3917", "3917 3917 1" ]
330342	2 3 55057	[ "330342 2 165171", "165171 3 55057", "55057 55057 1" ]
3225583	29 111227	[ "3225583 29 111227", "111227 111227 1" ]
580263	3 127 1523	[ "580263 3 193421", "193421 127 1523", "1523 1523 1" ]
218281	7 31183	[ "218281 7 31183", "31183 31183 1" ]
96215	5 7 2749	[ "96215 5 19243", "19243 7 2749", "2749 2749 1" ]
2768202	2 3 3 3 51263	[ "2768202 2 1384101", "1384101 3 461367", "461367 3 153789", "153789 3 51263", "51263 51263 1" ]
544001	544001	[ "544001 544001 1" ]
2019717	3 3 7 32059	[ "2019717 3 673239", "673239 3 224413", "224413 7 32059", "32059 32059 1" ]
2703406	2 1351703	[ "2703406 2 1351703", "1351703 1351703 1" ]
2102737	7 7 13 3301	[ "2102737 7 300391", "300391 7 42913", "42913 13 3301", "3301 3301 1" ]
69795	3 3 3 5 11 47	[ "69795 3 23265", "23265 3 7755", "7755 3 2585", "2585 5 517", "517 11 47", "47 47 1" ]
27981	3 3 3109	[ "27981 3 9327", "9327 3 3109", "3109 3109 1" ]
4536964	2 2 1134241	[ "4536964 2 2268482", "2268482 2 1134241", "1134241 1134241 1" ]
2644173	3 3 7 19 47 47	[ "2644173 3 881391", "881391 3 293797", "293797 7 41971", "41971 19 2209", "2209 47 47", "47 47 1" ]
1015687	37 97 283	[ "1015687 37 27451", "27451 97 283", "283 283 1" ]
566992	2 2 2 2 35437	[ "566992 2 283496", "283496 2 141748", "141748 2 70874", "70874 2 35437", "35437 35437 1" ]
2835090	2 3 3 5 17 17 109	[ "2835090 2 1417545", "1417545 3 472515", "472515 3 157505", "157505 5 31501", "31501 17 1853", "1853 17 109", "109 109 1" ]
1127194	2 19 29663	[ "1127194 2 563597", "563597 19 29663", "29663 29663 1" ]
1717511	443 3877	[ "1717511 443 3877", "3877 3877 1" ]
3635777	1637 2221	[ "3635777 1637 2221", "2221 2221 1" ]
4267364	2 2 67 15923	[ "4267364 2 2133682", "2133682 2 1066841", "1066841 67 15923", "15923 15923 1" ]
4366858	2 17 128437	[ "4366858 2 2183429", "2183429 17 128437", "128437 128437 1" ]
2005383	3 73 9157	[ "2005383 3 668461", "668461 73 9157", "9157 9157 1" ]
1641067	79 20773	[ "1641067 79 20773", "20773 20773 1" ]
939524	2 2 193 1217	[ "939524 2 469762", "469762 2 234881", "234881 193 1217", "1217 1217 1" ]
53225	5 5 2129	[ "53225 5 10645", "10645 5 2129", "2129 2129 1" ]
4131456	2 2 2 2 2 2 2 3 7 29 53	[ "4131456 2 2065728", "2065728 2 1032864", "1032864 2 516432", "516432 2 258216", "258216 2 129108", "129108 2 64554", "64554 2 32277", "32277 3 10759", "10759 7 1537", "1537 29 53", "53 53 1" ]
3665868	2 2 3 305489	[ "3665868 2 1832934", "1832934 2 916467", "916467 3 305489", "305489 305489 1" ]
2768912	2 2 2 2 61 2837	[ "2768912 2 1384456", "1384456 2 692228", "692228 2 346114", "346114 2 173057", "173057 61 2837", "2837 2837 1" ]
2028706	2 19 197 271	[ "2028706 2 1014353", "1014353 19 53387", "53387 197 271", "271 271 1" ]
4391788	2 2 1097947	[ "4391788 2 2195894", "2195894 2 1097947", "1097947 1097947 1" ]
3107163	3 761 1361	[ "3107163 3 1035721", "1035721 761 1361", "1361 1361 1" ]
1629779	911 1789	[ "1629779 911 1789", "1789 1789 1" ]
4552426	2 73 31181	[ "4552426 2 2276213", "2276213 73 31181", "31181 31181 1" ]
845826	2 3 61 2311	[ "845826 2 422913", "422913 3 140971", "140971 61 2311", "2311 2311 1" ]
2823772	2 2 7 7 14407	[ "2823772 2 1411886", "1411886 2 705943", "705943 7 100849", "100849 7 14407", "14407 14407 1" ]
1654508	2 2 17 29 839	[ "1654508 2 827254", "827254 2 413627", "413627 17 24331", "24331 29 839", "839 839 1" ]
1724149	7 23 10709	[ "1724149 7 246307", "246307 23 10709", "10709 10709 1" ]

1772115

3 5 31 37 103

[ "1772115 3 590705", "590705 5 118141", "118141 31 3811", "3811 37 103", "103 103 1" ]

3371868

2 2 3 3 3 3 3 3469

[ "3371868 2 1685934", "1685934 2 842967", "842967 3 280989", "280989 3 93663", "93663 3 31221", "31221 3 10407", "10407 3 3469", "3469 3469 1" ]

2212446

2 3 491 751

[ "2212446 2 1106223", "1106223 3 368741", "368741 491 751", "751 751 1" ]

2033276

2 2 7 72617

[ "2033276 2 1016638", "1016638 2 508319", "508319 7 72617", "72617 72617 1" ]

3735173

13 287321

[ "3735173 13 287321", "287321 287321 1" ]

3176296

2 2 2 397037

[ "3176296 2 1588148", "1588148 2 794074", "794074 2 397037", "397037 397037 1" ]

62771

41 1531

[ "62771 41 1531", "1531 1531 1" ]

3229607

239 13513

[ "3229607 239 13513", "13513 13513 1" ]

353069

[ "353069 353069 1" ]

1978133

401 4933

[ "1978133 401 4933", "4933 4933 1" ]

354277

7 11 43 107

[ "354277 7 50611", "50611 11 4601", "4601 43 107", "107 107 1" ]

3449362

2 7 37 6659

[ "3449362 2 1724681", "1724681 7 246383", "246383 37 6659", "6659 6659 1" ]

4245349

461 9209

[ "4245349 461 9209", "9209 9209 1" ]

2747575

5 5 109903

[ "2747575 5 549515", "549515 5 109903", "109903 109903 1" ]

3156807

3 1052269

[ "3156807 3 1052269", "1052269 1052269 1" ]

4588356

2 2 3 382363

[ "4588356 2 2294178", "2294178 2 1147089", "1147089 3 382363", "382363 382363 1" ]

4979327

41 121447

[ "4979327 41 121447", "121447 121447 1" ]

3362234

2 73 23029

[ "3362234 2 1681117", "1681117 73 23029", "23029 23029 1" ]

2492489

17 146617

[ "2492489 17 146617", "146617 146617 1" ]

3623339

61 59399

[ "3623339 61 59399", "59399 59399 1" ]

3406380

2 2 3 5 56773

[ "3406380 2 1703190", "1703190 2 851595", "851595 3 283865", "283865 5 56773", "56773 56773 1" ]

2987836

2 2 746959

[ "2987836 2 1493918", "1493918 2 746959", "746959 746959 1" ]

3475880

2 2 2 5 113 769

[ "3475880 2 1737940", "1737940 2 868970", "868970 2 434485", "434485 5 86897", "86897 113 769", "769 769 1" ]

2692716

2 2 3 13 41 421

[ "2692716 2 1346358", "1346358 2 673179", "673179 3 224393", "224393 13 17261", "17261 41 421", "421 421 1" ]

3768808

2 2 2 471101

[ "3768808 2 1884404", "1884404 2 942202", "942202 2 471101", "471101 471101 1" ]

4586166

2 3 3 3 13 47 139

[ "4586166 2 2293083", "2293083 3 764361", "764361 3 254787", "254787 3 84929", "84929 13 6533", "6533 47 139", "139 139 1" ]

1362619

[ "1362619 1362619 1" ]

1888567

29 65123

[ "1888567 29 65123", "65123 65123 1" ]

3276875

5 5 5 5 7 7 107

[ "3276875 5 655375", "655375 5 131075", "131075 5 26215", "26215 5 5243", "5243 7 749", "749 7 107", "107 107 1" ]

4619382

2 3 67 11491

[ "4619382 2 2309691", "2309691 3 769897", "769897 67 11491", "11491 11491 1" ]

1554384

2 2 2 2 3 13 47 53

[ "1554384 2 777192", "777192 2 388596", "388596 2 194298", "194298 2 97149", "97149 3 32383", "32383 13 2491", "2491 47 53", "53 53 1" ]

3205522

2 1602761

[ "3205522 2 1602761", "1602761 1602761 1" ]

3561139

37 109 883

[ "3561139 37 96247", "96247 109 883", "883 883 1" ]

2244850

2 5 5 17 19 139

[ "2244850 2 1122425", "1122425 5 224485", "224485 5 44897", "44897 17 2641", "2641 19 139", "139 139 1" ]

1231564

2 2 307891

[ "1231564 2 615782", "615782 2 307891", "307891 307891 1" ]

321243

3 13 8237

[ "321243 3 107081", "107081 13 8237", "8237 8237 1" ]

2487951

3 3 276439

[ "2487951 3 829317", "829317 3 276439", "276439 276439 1" ]

3409255

5 43 101 157

[ "3409255 5 681851", "681851 43 15857", "15857 101 157", "157 157 1" ]

230200

2 2 2 5 5 1151

[ "230200 2 115100", "115100 2 57550", "57550 2 28775", "28775 5 5755", "5755 5 1151", "1151 1151 1" ]

322836

2 2 3 26903

[ "322836 2 161418", "161418 2 80709", "80709 3 26903", "26903 26903 1" ]

2499959

7 11 32467

[ "2499959 7 357137", "357137 11 32467", "32467 32467 1" ]

3584017

[ "3584017 3584017 1" ]

1863579

3 37 103 163

[ "1863579 3 621193", "621193 37 16789", "16789 103 163", "163 163 1" ]

663583

[ "663583 663583 1" ]

531600

2 2 2 2 3 5 5 443

[ "531600 2 265800", "265800 2 132900", "132900 2 66450", "66450 2 33225", "33225 3 11075", "11075 5 2215", "2215 5 443", "443 443 1" ]

1900831

[ "1900831 1900831 1" ]

2803451

7 619 647

[ "2803451 7 400493", "400493 619 647", "647 647 1" ]

3239328

2 2 2 2 2 3 41 823

[ "3239328 2 1619664", "1619664 2 809832", "809832 2 404916", "404916 2 202458", "202458 2 101229", "101229 3 33743", "33743 41 823", "823 823 1" ]

1628052

2 2 3 135671

[ "1628052 2 814026", "814026 2 407013", "407013 3 135671", "135671 135671 1" ]

1171593

3 3 349 373

[ "1171593 3 390531", "390531 3 130177", "130177 349 373", "373 373 1" ]

585287

197 2971

[ "585287 197 2971", "2971 2971 1" ]

4240846

2 2120423

[ "4240846 2 2120423", "2120423 2120423 1" ]

2341879

41 57119

[ "2341879 41 57119", "57119 57119 1" ]

4844935

5 571 1697

[ "4844935 5 968987", "968987 571 1697", "1697 1697 1" ]

409609

[ "409609 409609 1" ]

4591765

5 918353

[ "4591765 5 918353", "918353 918353 1" ]

490290

2 3 5 59 277

[ "490290 2 245145", "245145 3 81715", "81715 5 16343", "16343 59 277", "277 277 1" ]

2062453

79 26107

[ "2062453 79 26107", "26107 26107 1" ]

2079731

83 25057

[ "2079731 83 25057", "25057 25057 1" ]

2712773

7 191 2029

[ "2712773 7 387539", "387539 191 2029", "2029 2029 1" ]

169664

2 2 2 2 2 2 11 241

[ "169664 2 84832", "84832 2 42416", "42416 2 21208", "21208 2 10604", "10604 2 5302", "5302 2 2651", "2651 11 241", "241 241 1" ]

266356

2 2 17 3917

[ "266356 2 133178", "133178 2 66589", "66589 17 3917", "3917 3917 1" ]

330342

2 3 55057

[ "330342 2 165171", "165171 3 55057", "55057 55057 1" ]

3225583

29 111227

[ "3225583 29 111227", "111227 111227 1" ]

580263

3 127 1523

[ "580263 3 193421", "193421 127 1523", "1523 1523 1" ]

218281

7 31183

[ "218281 7 31183", "31183 31183 1" ]

96215

5 7 2749

[ "96215 5 19243", "19243 7 2749", "2749 2749 1" ]

2768202

2 3 3 3 51263

[ "2768202 2 1384101", "1384101 3 461367", "461367 3 153789", "153789 3 51263", "51263 51263 1" ]

544001

[ "544001 544001 1" ]

2019717

3 3 7 32059

[ "2019717 3 673239", "673239 3 224413", "224413 7 32059", "32059 32059 1" ]

2703406

2 1351703

[ "2703406 2 1351703", "1351703 1351703 1" ]

2102737

7 7 13 3301

[ "2102737 7 300391", "300391 7 42913", "42913 13 3301", "3301 3301 1" ]

69795

3 3 3 5 11 47

[ "69795 3 23265", "23265 3 7755", "7755 3 2585", "2585 5 517", "517 11 47", "47 47 1" ]

27981

3 3 3109

[ "27981 3 9327", "9327 3 3109", "3109 3109 1" ]

4536964

2 2 1134241

[ "4536964 2 2268482", "2268482 2 1134241", "1134241 1134241 1" ]

2644173

3 3 7 19 47 47

[ "2644173 3 881391", "881391 3 293797", "293797 7 41971", "41971 19 2209", "2209 47 47", "47 47 1" ]

1015687

37 97 283

[ "1015687 37 27451", "27451 97 283", "283 283 1" ]

566992

2 2 2 2 35437

[ "566992 2 283496", "283496 2 141748", "141748 2 70874", "70874 2 35437", "35437 35437 1" ]

2835090

2 3 3 5 17 17 109

[ "2835090 2 1417545", "1417545 3 472515", "472515 3 157505", "157505 5 31501", "31501 17 1853", "1853 17 109", "109 109 1" ]

1127194

2 19 29663

[ "1127194 2 563597", "563597 19 29663", "29663 29663 1" ]

1717511

443 3877

[ "1717511 443 3877", "3877 3877 1" ]

3635777

1637 2221

[ "3635777 1637 2221", "2221 2221 1" ]

4267364

2 2 67 15923

[ "4267364 2 2133682", "2133682 2 1066841", "1066841 67 15923", "15923 15923 1" ]

4366858

2 17 128437

[ "4366858 2 2183429", "2183429 17 128437", "128437 128437 1" ]

2005383

3 73 9157

[ "2005383 3 668461", "668461 73 9157", "9157 9157 1" ]

1641067

79 20773

[ "1641067 79 20773", "20773 20773 1" ]

939524

2 2 193 1217

[ "939524 2 469762", "469762 2 234881", "234881 193 1217", "1217 1217 1" ]

53225

5 5 2129

[ "53225 5 10645", "10645 5 2129", "2129 2129 1" ]

4131456

2 2 2 2 2 2 2 3 7 29 53

[ "4131456 2 2065728", "2065728 2 1032864", "1032864 2 516432", "516432 2 258216", "258216 2 129108", "129108 2 64554", "64554 2 32277", "32277 3 10759", "10759 7 1537", "1537 29 53", "53 53 1" ]

3665868

2 2 3 305489

[ "3665868 2 1832934", "1832934 2 916467", "916467 3 305489", "305489 305489 1" ]

2768912

2 2 2 2 61 2837

[ "2768912 2 1384456", "1384456 2 692228", "692228 2 346114", "346114 2 173057", "173057 61 2837", "2837 2837 1" ]

2028706

2 19 197 271

[ "2028706 2 1014353", "1014353 19 53387", "53387 197 271", "271 271 1" ]

4391788

2 2 1097947

[ "4391788 2 2195894", "2195894 2 1097947", "1097947 1097947 1" ]

3107163

3 761 1361

[ "3107163 3 1035721", "1035721 761 1361", "1361 1361 1" ]

1629779

911 1789

[ "1629779 911 1789", "1789 1789 1" ]

4552426

2 73 31181

[ "4552426 2 2276213", "2276213 73 31181", "31181 31181 1" ]

845826

2 3 61 2311

[ "845826 2 422913", "422913 3 140971", "140971 61 2311", "2311 2311 1" ]

2823772

2 2 7 7 14407

[ "2823772 2 1411886", "1411886 2 705943", "705943 7 100849", "100849 7 14407", "14407 14407 1" ]

1654508

2 2 17 29 839

[ "1654508 2 827254", "827254 2 413627", "413627 17 24331", "24331 29 839", "839 839 1" ]

1724149

7 23 10709

[ "1724149 7 246307", "246307 23 10709", "10709 10709 1" ]