yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
4433045	5 886609	[ "4433045 5 886609", "886609 886609 1" ]
4327915	5 19 45557	[ "4327915 5 865583", "865583 19 45557", "45557 45557 1" ]
142032	2 2 2 2 3 11 269	[ "142032 2 71016", "71016 2 35508", "35508 2 17754", "17754 2 8877", "8877 3 2959", "2959 11 269", "269 269 1" ]
1405995	3 5 67 1399	[ "1405995 3 468665", "468665 5 93733", "93733 67 1399", "1399 1399 1" ]
949612	2 2 43 5521	[ "949612 2 474806", "474806 2 237403", "237403 43 5521", "5521 5521 1" ]
1565237	223 7019	[ "1565237 223 7019", "7019 7019 1" ]
1887606	2 3 3 7 71 211	[ "1887606 2 943803", "943803 3 314601", "314601 3 104867", "104867 7 14981", "14981 71 211", "211 211 1" ]
2126112	2 2 2 2 2 3 22147	[ "2126112 2 1063056", "1063056 2 531528", "531528 2 265764", "265764 2 132882", "132882 2 66441", "66441 3 22147", "22147 22147 1" ]
11255	5 2251	[ "11255 5 2251", "2251 2251 1" ]
3906539	7 13 42929	[ "3906539 7 558077", "558077 13 42929", "42929 42929 1" ]
3873045	3 5 11 23473	[ "3873045 3 1291015", "1291015 5 258203", "258203 11 23473", "23473 23473 1" ]
3739257	3 3 3 19 37 197	[ "3739257 3 1246419", "1246419 3 415473", "415473 3 138491", "138491 19 7289", "7289 37 197", "197 197 1" ]
4536859	4536859	[ "4536859 4536859 1" ]
3311416	2 2 2 359 1153	[ "3311416 2 1655708", "1655708 2 827854", "827854 2 413927", "413927 359 1153", "1153 1153 1" ]
4842991	659 7349	[ "4842991 659 7349", "7349 7349 1" ]
3707377	17 218081	[ "3707377 17 218081", "218081 218081 1" ]
2966953	11 269723	[ "2966953 11 269723", "269723 269723 1" ]
3970648	2 2 2 11 45121	[ "3970648 2 1985324", "1985324 2 992662", "992662 2 496331", "496331 11 45121", "45121 45121 1" ]
333991	7 47713	[ "333991 7 47713", "47713 47713 1" ]
2053079	7 241 1217	[ "2053079 7 293297", "293297 241 1217", "1217 1217 1" ]
1279766	2 23 43 647	[ "1279766 2 639883", "639883 23 27821", "27821 43 647", "647 647 1" ]
694945	5 23 6043	[ "694945 5 138989", "138989 23 6043", "6043 6043 1" ]
52583	52583	[ "52583 52583 1" ]
3980858	2 7 7 7 7 829	[ "3980858 2 1990429", "1990429 7 284347", "284347 7 40621", "40621 7 5803", "5803 7 829", "829 829 1" ]
2971912	2 2 2 269 1381	[ "2971912 2 1485956", "1485956 2 742978", "742978 2 371489", "371489 269 1381", "1381 1381 1" ]
1182943	47 25169	[ "1182943 47 25169", "25169 25169 1" ]
1100894	2 550447	[ "1100894 2 550447", "550447 550447 1" ]
3073675	5 5 11 11177	[ "3073675 5 614735", "614735 5 122947", "122947 11 11177", "11177 11177 1" ]
4715111	4715111	[ "4715111 4715111 1" ]
4377530	2 5 437753	[ "4377530 2 2188765", "2188765 5 437753", "437753 437753 1" ]
1319639	31 42569	[ "1319639 31 42569", "42569 42569 1" ]
1174547	11 11 17 571	[ "1174547 11 106777", "106777 11 9707", "9707 17 571", "571 571 1" ]
3358915	5 7 19 5051	[ "3358915 5 671783", "671783 7 95969", "95969 19 5051", "5051 5051 1" ]
3904397	7 541 1031	[ "3904397 7 557771", "557771 541 1031", "1031 1031 1" ]
2585226	2 3 7 61553	[ "2585226 2 1292613", "1292613 3 430871", "430871 7 61553", "61553 61553 1" ]
744562	2 7 13 4091	[ "744562 2 372281", "372281 7 53183", "53183 13 4091", "4091 4091 1" ]
4321963	223 19381	[ "4321963 223 19381", "19381 19381 1" ]
3986947	1381 2887	[ "3986947 1381 2887", "2887 2887 1" ]
4990508	2 2 1247627	[ "4990508 2 2495254", "2495254 2 1247627", "1247627 1247627 1" ]
2352545	5 13 17 2129	[ "2352545 5 470509", "470509 13 36193", "36193 17 2129", "2129 2129 1" ]
453416	2 2 2 19 19 157	[ "453416 2 226708", "226708 2 113354", "113354 2 56677", "56677 19 2983", "2983 19 157", "157 157 1" ]
2066882	2 1033441	[ "2066882 2 1033441", "1033441 1033441 1" ]
1030162	2 7 73583	[ "1030162 2 515081", "515081 7 73583", "73583 73583 1" ]
1431149	1431149	[ "1431149 1431149 1" ]
2925485	5 23 25439	[ "2925485 5 585097", "585097 23 25439", "25439 25439 1" ]
3718583	11 29 11657	[ "3718583 11 338053", "338053 29 11657", "11657 11657 1" ]
3944707	13 23 79 167	[ "3944707 13 303439", "303439 23 13193", "13193 79 167", "167 167 1" ]
364045	5 11 6619	[ "364045 5 72809", "72809 11 6619", "6619 6619 1" ]
3734591	7 29 18397	[ "3734591 7 533513", "533513 29 18397", "18397 18397 1" ]
2110144	2 2 2 2 2 2 32971	[ "2110144 2 1055072", "1055072 2 527536", "527536 2 263768", "263768 2 131884", "131884 2 65942", "65942 2 32971", "32971 32971 1" ]
4670960	2 2 2 2 5 7 19 439	[ "4670960 2 2335480", "2335480 2 1167740", "1167740 2 583870", "583870 2 291935", "291935 5 58387", "58387 7 8341", "8341 19 439", "439 439 1" ]
2454758	2 1227379	[ "2454758 2 1227379", "1227379 1227379 1" ]
4316353	983 4391	[ "4316353 983 4391", "4391 4391 1" ]
2347920	2 2 2 2 3 3 3 5 1087	[ "2347920 2 1173960", "1173960 2 586980", "586980 2 293490", "293490 2 146745", "146745 3 48915", "48915 3 16305", "16305 3 5435", "5435 5 1087", "1087 1087 1" ]
4775675	5 5 191027	[ "4775675 5 955135", "955135 5 191027", "191027 191027 1" ]
4734023	7 676289	[ "4734023 7 676289", "676289 676289 1" ]
1140411	3 17 59 379	[ "1140411 3 380137", "380137 17 22361", "22361 59 379", "379 379 1" ]
2658646	2 277 4799	[ "2658646 2 1329323", "1329323 277 4799", "4799 4799 1" ]
2446438	2 67 18257	[ "2446438 2 1223219", "1223219 67 18257", "18257 18257 1" ]
1927652	2 2 139 3467	[ "1927652 2 963826", "963826 2 481913", "481913 139 3467", "3467 3467 1" ]
1829258	2 914629	[ "1829258 2 914629", "914629 914629 1" ]
4217130	2 3 3 3 5 15619	[ "4217130 2 2108565", "2108565 3 702855", "702855 3 234285", "234285 3 78095", "78095 5 15619", "15619 15619 1" ]
4170175	5 5 166807	[ "4170175 5 834035", "834035 5 166807", "166807 166807 1" ]
699819	3 479 487	[ "699819 3 233273", "233273 479 487", "487 487 1" ]
1815211	127 14293	[ "1815211 127 14293", "14293 14293 1" ]
2641193	2641193	[ "2641193 2641193 1" ]
1436625	3 3 5 5 5 1277	[ "1436625 3 478875", "478875 3 159625", "159625 5 31925", "31925 5 6385", "6385 5 1277", "1277 1277 1" ]
2487974	2 19 233 281	[ "2487974 2 1243987", "1243987 19 65473", "65473 233 281", "281 281 1" ]
4951867	4951867	[ "4951867 4951867 1" ]
387297	3 3 23 1871	[ "387297 3 129099", "129099 3 43033", "43033 23 1871", "1871 1871 1" ]
4586837	59 77743	[ "4586837 59 77743", "77743 77743 1" ]
30285	3 3 5 673	[ "30285 3 10095", "10095 3 3365", "3365 5 673", "673 673 1" ]
4916827	4916827	[ "4916827 4916827 1" ]
143079	3 37 1289	[ "143079 3 47693", "47693 37 1289", "1289 1289 1" ]
1982653	89 22277	[ "1982653 89 22277", "22277 22277 1" ]
4998271	53 94307	[ "4998271 53 94307", "94307 94307 1" ]
2692057	397 6781	[ "2692057 397 6781", "6781 6781 1" ]
2385502	2 7 170393	[ "2385502 2 1192751", "1192751 7 170393", "170393 170393 1" ]
4306916	2 2 17 63337	[ "4306916 2 2153458", "2153458 2 1076729", "1076729 17 63337", "63337 63337 1" ]
1297414	2 223 2909	[ "1297414 2 648707", "648707 223 2909", "2909 2909 1" ]
2280463	2280463	[ "2280463 2280463 1" ]
3723470	2 5 23 16189	[ "3723470 2 1861735", "1861735 5 372347", "372347 23 16189", "16189 16189 1" ]
1048351	1009 1039	[ "1048351 1009 1039", "1039 1039 1" ]
1542797	43 35879	[ "1542797 43 35879", "35879 35879 1" ]
1441467	3 3 160163	[ "1441467 3 480489", "480489 3 160163", "160163 160163 1" ]
2184651	3 3 3 3 7 3853	[ "2184651 3 728217", "728217 3 242739", "242739 3 80913", "80913 3 26971", "26971 7 3853", "3853 3853 1" ]
2695045	5 539009	[ "2695045 5 539009", "539009 539009 1" ]
4508858	2 449 5021	[ "4508858 2 2254429", "2254429 449 5021", "5021 5021 1" ]
2859239	113 25303	[ "2859239 113 25303", "25303 25303 1" ]
3159687	3 223 4723	[ "3159687 3 1053229", "1053229 223 4723", "4723 4723 1" ]
284923	71 4013	[ "284923 71 4013", "4013 4013 1" ]
3283364	2 2 7 149 787	[ "3283364 2 1641682", "1641682 2 820841", "820841 7 117263", "117263 149 787", "787 787 1" ]
3211005	3 5 7 53 577	[ "3211005 3 1070335", "1070335 5 214067", "214067 7 30581", "30581 53 577", "577 577 1" ]
2649810	2 3 5 88327	[ "2649810 2 1324905", "1324905 3 441635", "441635 5 88327", "88327 88327 1" ]
3129963	3 263 3967	[ "3129963 3 1043321", "1043321 263 3967", "3967 3967 1" ]
2429807	281 8647	[ "2429807 281 8647", "8647 8647 1" ]
3714134	2 37 53 947	[ "3714134 2 1857067", "1857067 37 50191", "50191 53 947", "947 947 1" ]
2704767	3 13 223 311	[ "2704767 3 901589", "901589 13 69353", "69353 223 311", "311 311 1" ]
67792	2 2 2 2 19 223	[ "67792 2 33896", "33896 2 16948", "16948 2 8474", "8474 2 4237", "4237 19 223", "223 223 1" ]
3504860	2 2 5 31 5653	[ "3504860 2 1752430", "1752430 2 876215", "876215 5 175243", "175243 31 5653", "5653 5653 1" ]

4433045

5 886609

[ "4433045 5 886609", "886609 886609 1" ]

4327915

5 19 45557

[ "4327915 5 865583", "865583 19 45557", "45557 45557 1" ]

142032

2 2 2 2 3 11 269

[ "142032 2 71016", "71016 2 35508", "35508 2 17754", "17754 2 8877", "8877 3 2959", "2959 11 269", "269 269 1" ]

1405995

3 5 67 1399

[ "1405995 3 468665", "468665 5 93733", "93733 67 1399", "1399 1399 1" ]

949612

2 2 43 5521

[ "949612 2 474806", "474806 2 237403", "237403 43 5521", "5521 5521 1" ]

1565237

223 7019

[ "1565237 223 7019", "7019 7019 1" ]

1887606

2 3 3 7 71 211

[ "1887606 2 943803", "943803 3 314601", "314601 3 104867", "104867 7 14981", "14981 71 211", "211 211 1" ]

2126112

2 2 2 2 2 3 22147

[ "2126112 2 1063056", "1063056 2 531528", "531528 2 265764", "265764 2 132882", "132882 2 66441", "66441 3 22147", "22147 22147 1" ]

11255

5 2251

[ "11255 5 2251", "2251 2251 1" ]

3906539

7 13 42929

[ "3906539 7 558077", "558077 13 42929", "42929 42929 1" ]

3873045

3 5 11 23473

[ "3873045 3 1291015", "1291015 5 258203", "258203 11 23473", "23473 23473 1" ]

3739257

3 3 3 19 37 197

[ "3739257 3 1246419", "1246419 3 415473", "415473 3 138491", "138491 19 7289", "7289 37 197", "197 197 1" ]

4536859

[ "4536859 4536859 1" ]

3311416

2 2 2 359 1153

[ "3311416 2 1655708", "1655708 2 827854", "827854 2 413927", "413927 359 1153", "1153 1153 1" ]

4842991

659 7349

[ "4842991 659 7349", "7349 7349 1" ]

3707377

17 218081

[ "3707377 17 218081", "218081 218081 1" ]

2966953

11 269723

[ "2966953 11 269723", "269723 269723 1" ]

3970648

2 2 2 11 45121

[ "3970648 2 1985324", "1985324 2 992662", "992662 2 496331", "496331 11 45121", "45121 45121 1" ]

333991

7 47713

[ "333991 7 47713", "47713 47713 1" ]

2053079

7 241 1217

[ "2053079 7 293297", "293297 241 1217", "1217 1217 1" ]

1279766

2 23 43 647

[ "1279766 2 639883", "639883 23 27821", "27821 43 647", "647 647 1" ]

694945

5 23 6043

[ "694945 5 138989", "138989 23 6043", "6043 6043 1" ]

52583

[ "52583 52583 1" ]

3980858

2 7 7 7 7 829

[ "3980858 2 1990429", "1990429 7 284347", "284347 7 40621", "40621 7 5803", "5803 7 829", "829 829 1" ]

2971912

2 2 2 269 1381

[ "2971912 2 1485956", "1485956 2 742978", "742978 2 371489", "371489 269 1381", "1381 1381 1" ]

1182943

47 25169

[ "1182943 47 25169", "25169 25169 1" ]

1100894

2 550447

[ "1100894 2 550447", "550447 550447 1" ]

3073675

5 5 11 11177

[ "3073675 5 614735", "614735 5 122947", "122947 11 11177", "11177 11177 1" ]

4715111

[ "4715111 4715111 1" ]

4377530

2 5 437753

[ "4377530 2 2188765", "2188765 5 437753", "437753 437753 1" ]

1319639

31 42569

[ "1319639 31 42569", "42569 42569 1" ]

1174547

11 11 17 571

[ "1174547 11 106777", "106777 11 9707", "9707 17 571", "571 571 1" ]

3358915

5 7 19 5051

[ "3358915 5 671783", "671783 7 95969", "95969 19 5051", "5051 5051 1" ]

3904397

7 541 1031

[ "3904397 7 557771", "557771 541 1031", "1031 1031 1" ]

2585226

2 3 7 61553

[ "2585226 2 1292613", "1292613 3 430871", "430871 7 61553", "61553 61553 1" ]

744562

2 7 13 4091

[ "744562 2 372281", "372281 7 53183", "53183 13 4091", "4091 4091 1" ]

4321963

223 19381

[ "4321963 223 19381", "19381 19381 1" ]

3986947

1381 2887

[ "3986947 1381 2887", "2887 2887 1" ]

4990508

2 2 1247627

[ "4990508 2 2495254", "2495254 2 1247627", "1247627 1247627 1" ]

2352545

5 13 17 2129

[ "2352545 5 470509", "470509 13 36193", "36193 17 2129", "2129 2129 1" ]

453416

2 2 2 19 19 157

[ "453416 2 226708", "226708 2 113354", "113354 2 56677", "56677 19 2983", "2983 19 157", "157 157 1" ]

2066882

2 1033441

[ "2066882 2 1033441", "1033441 1033441 1" ]

1030162

2 7 73583

[ "1030162 2 515081", "515081 7 73583", "73583 73583 1" ]

1431149

[ "1431149 1431149 1" ]

2925485

5 23 25439

[ "2925485 5 585097", "585097 23 25439", "25439 25439 1" ]

3718583

11 29 11657

[ "3718583 11 338053", "338053 29 11657", "11657 11657 1" ]

3944707

13 23 79 167

[ "3944707 13 303439", "303439 23 13193", "13193 79 167", "167 167 1" ]

364045

5 11 6619

[ "364045 5 72809", "72809 11 6619", "6619 6619 1" ]

3734591

7 29 18397

[ "3734591 7 533513", "533513 29 18397", "18397 18397 1" ]

2110144

2 2 2 2 2 2 32971

[ "2110144 2 1055072", "1055072 2 527536", "527536 2 263768", "263768 2 131884", "131884 2 65942", "65942 2 32971", "32971 32971 1" ]

4670960

2 2 2 2 5 7 19 439

[ "4670960 2 2335480", "2335480 2 1167740", "1167740 2 583870", "583870 2 291935", "291935 5 58387", "58387 7 8341", "8341 19 439", "439 439 1" ]

2454758

2 1227379

[ "2454758 2 1227379", "1227379 1227379 1" ]

4316353

983 4391

[ "4316353 983 4391", "4391 4391 1" ]

2347920

2 2 2 2 3 3 3 5 1087

[ "2347920 2 1173960", "1173960 2 586980", "586980 2 293490", "293490 2 146745", "146745 3 48915", "48915 3 16305", "16305 3 5435", "5435 5 1087", "1087 1087 1" ]

4775675

5 5 191027

[ "4775675 5 955135", "955135 5 191027", "191027 191027 1" ]

4734023

7 676289

[ "4734023 7 676289", "676289 676289 1" ]

1140411

3 17 59 379

[ "1140411 3 380137", "380137 17 22361", "22361 59 379", "379 379 1" ]

2658646

2 277 4799

[ "2658646 2 1329323", "1329323 277 4799", "4799 4799 1" ]

2446438

2 67 18257

[ "2446438 2 1223219", "1223219 67 18257", "18257 18257 1" ]

1927652

2 2 139 3467

[ "1927652 2 963826", "963826 2 481913", "481913 139 3467", "3467 3467 1" ]

1829258

2 914629

[ "1829258 2 914629", "914629 914629 1" ]

4217130

2 3 3 3 5 15619

[ "4217130 2 2108565", "2108565 3 702855", "702855 3 234285", "234285 3 78095", "78095 5 15619", "15619 15619 1" ]

4170175

5 5 166807

[ "4170175 5 834035", "834035 5 166807", "166807 166807 1" ]

699819

3 479 487

[ "699819 3 233273", "233273 479 487", "487 487 1" ]

1815211

127 14293

[ "1815211 127 14293", "14293 14293 1" ]

2641193

[ "2641193 2641193 1" ]

1436625

3 3 5 5 5 1277

[ "1436625 3 478875", "478875 3 159625", "159625 5 31925", "31925 5 6385", "6385 5 1277", "1277 1277 1" ]

2487974

2 19 233 281

[ "2487974 2 1243987", "1243987 19 65473", "65473 233 281", "281 281 1" ]

4951867

[ "4951867 4951867 1" ]

387297

3 3 23 1871

[ "387297 3 129099", "129099 3 43033", "43033 23 1871", "1871 1871 1" ]

4586837

59 77743

[ "4586837 59 77743", "77743 77743 1" ]

30285

3 3 5 673

[ "30285 3 10095", "10095 3 3365", "3365 5 673", "673 673 1" ]

4916827

[ "4916827 4916827 1" ]

143079

3 37 1289

[ "143079 3 47693", "47693 37 1289", "1289 1289 1" ]

1982653

89 22277

[ "1982653 89 22277", "22277 22277 1" ]

4998271

53 94307

[ "4998271 53 94307", "94307 94307 1" ]

2692057

397 6781

[ "2692057 397 6781", "6781 6781 1" ]

2385502

2 7 170393

[ "2385502 2 1192751", "1192751 7 170393", "170393 170393 1" ]

4306916

2 2 17 63337

[ "4306916 2 2153458", "2153458 2 1076729", "1076729 17 63337", "63337 63337 1" ]

1297414

2 223 2909

[ "1297414 2 648707", "648707 223 2909", "2909 2909 1" ]

2280463

[ "2280463 2280463 1" ]

3723470

2 5 23 16189

[ "3723470 2 1861735", "1861735 5 372347", "372347 23 16189", "16189 16189 1" ]

1048351

1009 1039

[ "1048351 1009 1039", "1039 1039 1" ]

1542797

43 35879

[ "1542797 43 35879", "35879 35879 1" ]

1441467

3 3 160163

[ "1441467 3 480489", "480489 3 160163", "160163 160163 1" ]

2184651

3 3 3 3 7 3853

[ "2184651 3 728217", "728217 3 242739", "242739 3 80913", "80913 3 26971", "26971 7 3853", "3853 3853 1" ]

2695045

5 539009

[ "2695045 5 539009", "539009 539009 1" ]

4508858

2 449 5021

[ "4508858 2 2254429", "2254429 449 5021", "5021 5021 1" ]

2859239

113 25303

[ "2859239 113 25303", "25303 25303 1" ]

3159687

3 223 4723

[ "3159687 3 1053229", "1053229 223 4723", "4723 4723 1" ]

284923

71 4013

[ "284923 71 4013", "4013 4013 1" ]

3283364

2 2 7 149 787

[ "3283364 2 1641682", "1641682 2 820841", "820841 7 117263", "117263 149 787", "787 787 1" ]

3211005

3 5 7 53 577

[ "3211005 3 1070335", "1070335 5 214067", "214067 7 30581", "30581 53 577", "577 577 1" ]

2649810

2 3 5 88327

[ "2649810 2 1324905", "1324905 3 441635", "441635 5 88327", "88327 88327 1" ]

3129963

3 263 3967

[ "3129963 3 1043321", "1043321 263 3967", "3967 3967 1" ]

2429807

281 8647

[ "2429807 281 8647", "8647 8647 1" ]

3714134

2 37 53 947

[ "3714134 2 1857067", "1857067 37 50191", "50191 53 947", "947 947 1" ]

2704767

3 13 223 311

[ "2704767 3 901589", "901589 13 69353", "69353 223 311", "311 311 1" ]

67792

2 2 2 2 19 223

[ "67792 2 33896", "33896 2 16948", "16948 2 8474", "8474 2 4237", "4237 19 223", "223 223 1" ]

3504860

2 2 5 31 5653

[ "3504860 2 1752430", "1752430 2 876215", "876215 5 175243", "175243 31 5653", "5653 5653 1" ]