yimingzhang/prime-factorization · Datasets at Hugging Face

input stringlengths 3 7	output stringlengths 3 41	step_by_step_solution listlengths 1 21
140176	2 2 2 2 8761	[ "140176 2 70088", "70088 2 35044", "35044 2 17522", "17522 2 8761", "8761 8761 1" ]
3733348	2 2 19 49123	[ "3733348 2 1866674", "1866674 2 933337", "933337 19 49123", "49123 49123 1" ]
3733611	3 7 177791	[ "3733611 3 1244537", "1244537 7 177791", "177791 177791 1" ]
3014698	2 173 8713	[ "3014698 2 1507349", "1507349 173 8713", "8713 8713 1" ]
1859003	191 9733	[ "1859003 191 9733", "9733 9733 1" ]
2324746	2 1162373	[ "2324746 2 1162373", "1162373 1162373 1" ]
662946	2 3 110491	[ "662946 2 331473", "331473 3 110491", "110491 110491 1" ]
3346546	2 7 19 23 547	[ "3346546 2 1673273", "1673273 7 239039", "239039 19 12581", "12581 23 547", "547 547 1" ]
855774	2 3 3 47543	[ "855774 2 427887", "427887 3 142629", "142629 3 47543", "47543 47543 1" ]
2094601	2094601	[ "2094601 2094601 1" ]
4905327	3 7 109 2143	[ "4905327 3 1635109", "1635109 7 233587", "233587 109 2143", "2143 2143 1" ]
1318405	5 11 23971	[ "1318405 5 263681", "263681 11 23971", "23971 23971 1" ]
1721462	2 37 43 541	[ "1721462 2 860731", "860731 37 23263", "23263 43 541", "541 541 1" ]
3013558	2 1506779	[ "3013558 2 1506779", "1506779 1506779 1" ]
4987462	2 19 131249	[ "4987462 2 2493731", "2493731 19 131249", "131249 131249 1" ]
4212626	2 11 419 457	[ "4212626 2 2106313", "2106313 11 191483", "191483 419 457", "457 457 1" ]
1266499	13 97423	[ "1266499 13 97423", "97423 97423 1" ]
3453374	2 53 32579	[ "3453374 2 1726687", "1726687 53 32579", "32579 32579 1" ]
826585	5 165317	[ "826585 5 165317", "165317 165317 1" ]
4459837	823 5419	[ "4459837 823 5419", "5419 5419 1" ]
4886144	2 2 2 2 2 2 2 59 647	[ "4886144 2 2443072", "2443072 2 1221536", "1221536 2 610768", "610768 2 305384", "305384 2 152692", "152692 2 76346", "76346 2 38173", "38173 59 647", "647 647 1" ]
4856120	2 2 2 5 121403	[ "4856120 2 2428060", "2428060 2 1214030", "1214030 2 607015", "607015 5 121403", "121403 121403 1" ]
4815680	2 2 2 2 2 2 5 101 149	[ "4815680 2 2407840", "2407840 2 1203920", "1203920 2 601960", "601960 2 300980", "300980 2 150490", "150490 2 75245", "75245 5 15049", "15049 101 149", "149 149 1" ]
801152	2 2 2 2 2 2 2 11 569	[ "801152 2 400576", "400576 2 200288", "200288 2 100144", "100144 2 50072", "50072 2 25036", "25036 2 12518", "12518 2 6259", "6259 11 569", "569 569 1" ]
4082025	3 5 5 37 1471	[ "4082025 3 1360675", "1360675 5 272135", "272135 5 54427", "54427 37 1471", "1471 1471 1" ]
2865176	2 2 2 43 8329	[ "2865176 2 1432588", "1432588 2 716294", "716294 2 358147", "358147 43 8329", "8329 8329 1" ]
3595773	3 113 10607	[ "3595773 3 1198591", "1198591 113 10607", "10607 10607 1" ]
4239437	1487 2851	[ "4239437 1487 2851", "2851 2851 1" ]
2141028	2 2 3 3 59473	[ "2141028 2 1070514", "1070514 2 535257", "535257 3 178419", "178419 3 59473", "59473 59473 1" ]
940345	5 7 67 401	[ "940345 5 188069", "188069 7 26867", "26867 67 401", "401 401 1" ]
4586833	4586833	[ "4586833 4586833 1" ]
2099449	11 17 103 109	[ "2099449 11 190859", "190859 17 11227", "11227 103 109", "109 109 1" ]
3001549	53 56633	[ "3001549 53 56633", "56633 56633 1" ]
4089543	3 251 5431	[ "4089543 3 1363181", "1363181 251 5431", "5431 5431 1" ]
1726915	5 569 607	[ "1726915 5 345383", "345383 569 607", "607 607 1" ]
3295458	2 3 3 3 61027	[ "3295458 2 1647729", "1647729 3 549243", "549243 3 183081", "183081 3 61027", "61027 61027 1" ]
3593387	7 513341	[ "3593387 7 513341", "513341 513341 1" ]
2700532	2 2 675133	[ "2700532 2 1350266", "1350266 2 675133", "675133 675133 1" ]
4079724	2 2 3 11 31 997	[ "4079724 2 2039862", "2039862 2 1019931", "1019931 3 339977", "339977 11 30907", "30907 31 997", "997 997 1" ]
264619	264619	[ "264619 264619 1" ]
4378755	3 5 47 6211	[ "4378755 3 1459585", "1459585 5 291917", "291917 47 6211", "6211 6211 1" ]
927592	2 2 2 47 2467	[ "927592 2 463796", "463796 2 231898", "231898 2 115949", "115949 47 2467", "2467 2467 1" ]
660545	5 132109	[ "660545 5 132109", "132109 132109 1" ]
4101418	2 211 9719	[ "4101418 2 2050709", "2050709 211 9719", "9719 9719 1" ]
2147965	5 269 1597	[ "2147965 5 429593", "429593 269 1597", "1597 1597 1" ]
2711596	2 2 79 8581	[ "2711596 2 1355798", "1355798 2 677899", "677899 79 8581", "8581 8581 1" ]
2026106	2 1013053	[ "2026106 2 1013053", "1013053 1013053 1" ]
3849218	2 107 17987	[ "3849218 2 1924609", "1924609 107 17987", "17987 17987 1" ]
1169540	2 2 5 58477	[ "1169540 2 584770", "584770 2 292385", "292385 5 58477", "58477 58477 1" ]
1986011	541 3671	[ "1986011 541 3671", "3671 3671 1" ]
4241299	109 167 233	[ "4241299 109 38911", "38911 167 233", "233 233 1" ]
4554418	2 11 241 859	[ "4554418 2 2277209", "2277209 11 207019", "207019 241 859", "859 859 1" ]
2957577	3 7 140837	[ "2957577 3 985859", "985859 7 140837", "140837 140837 1" ]
4600887	3 1533629	[ "4600887 3 1533629", "1533629 1533629 1" ]
2901054	2 3 13 13 2861	[ "2901054 2 1450527", "1450527 3 483509", "483509 13 37193", "37193 13 2861", "2861 2861 1" ]
2260145	5 19 37 643	[ "2260145 5 452029", "452029 19 23791", "23791 37 643", "643 643 1" ]
239287	239287	[ "239287 239287 1" ]
3630974	2 29 62603	[ "3630974 2 1815487", "1815487 29 62603", "62603 62603 1" ]
2763098	2 13 106273	[ "2763098 2 1381549", "1381549 13 106273", "106273 106273 1" ]
4050534	2 3 19 35531	[ "4050534 2 2025267", "2025267 3 675089", "675089 19 35531", "35531 35531 1" ]
1587306	2 3 7 7 5399	[ "1587306 2 793653", "793653 3 264551", "264551 7 37793", "37793 7 5399", "5399 5399 1" ]
689317	689317	[ "689317 689317 1" ]
1141760	2 2 2 2 2 2 2 2 2 2 5 223	[ "1141760 2 570880", "570880 2 285440", "285440 2 142720", "142720 2 71360", "71360 2 35680", "35680 2 17840", "17840 2 8920", "8920 2 4460", "4460 2 2230", "2230 2 1115", "1115 5 223", "223 223 1" ]
1685908	2 2 7 19 3169	[ "1685908 2 842954", "842954 2 421477", "421477 7 60211", "60211 19 3169", "3169 3169 1" ]
4561331	4561331	[ "4561331 4561331 1" ]
4697642	2 173 13577	[ "4697642 2 2348821", "2348821 173 13577", "13577 13577 1" ]
2929199	7 13 32189	[ "2929199 7 418457", "418457 13 32189", "32189 32189 1" ]
3698259	3 367 3359	[ "3698259 3 1232753", "1232753 367 3359", "3359 3359 1" ]
4667878	2 2333939	[ "4667878 2 2333939", "2333939 2333939 1" ]
3934553	7 7 7 11471	[ "3934553 7 562079", "562079 7 80297", "80297 7 11471", "11471 11471 1" ]
4735380	2 2 3 5 13 13 467	[ "4735380 2 2367690", "2367690 2 1183845", "1183845 3 394615", "394615 5 78923", "78923 13 6071", "6071 13 467", "467 467 1" ]
438701	438701	[ "438701 438701 1" ]
3106076	2 2 31 37 677	[ "3106076 2 1553038", "1553038 2 776519", "776519 31 25049", "25049 37 677", "677 677 1" ]
3633653	3633653	[ "3633653 3633653 1" ]
1538998	2 373 2063	[ "1538998 2 769499", "769499 373 2063", "2063 2063 1" ]
1784759	541 3299	[ "1784759 541 3299", "3299 3299 1" ]
3036723	3 1012241	[ "3036723 3 1012241", "1012241 1012241 1" ]
2274413	17 337 397	[ "2274413 17 133789", "133789 337 397", "397 397 1" ]
952632	2 2 2 3 3 101 131	[ "952632 2 476316", "476316 2 238158", "238158 2 119079", "119079 3 39693", "39693 3 13231", "13231 101 131", "131 131 1" ]
4103433	3 3 3 379 401	[ "4103433 3 1367811", "1367811 3 455937", "455937 3 151979", "151979 379 401", "401 401 1" ]
4550591	4550591	[ "4550591 4550591 1" ]
3583364	2 2 895841	[ "3583364 2 1791682", "1791682 2 895841", "895841 895841 1" ]
2857509	3 3 79 4019	[ "2857509 3 952503", "952503 3 317501", "317501 79 4019", "4019 4019 1" ]
1598553	3 3 11 67 241	[ "1598553 3 532851", "532851 3 177617", "177617 11 16147", "16147 67 241", "241 241 1" ]
4625699	13 13 101 271	[ "4625699 13 355823", "355823 13 27371", "27371 101 271", "271 271 1" ]
1032942	2 3 172157	[ "1032942 2 516471", "516471 3 172157", "172157 172157 1" ]
3651113	139 26267	[ "3651113 139 26267", "26267 26267 1" ]
559971	3 3 62219	[ "559971 3 186657", "186657 3 62219", "62219 62219 1" ]
2095546	2 1047773	[ "2095546 2 1047773", "1047773 1047773 1" ]
954825	3 5 5 29 439	[ "954825 3 318275", "318275 5 63655", "63655 5 12731", "12731 29 439", "439 439 1" ]
253553	253553	[ "253553 253553 1" ]
1753038	2 3 3 7 13913	[ "1753038 2 876519", "876519 3 292173", "292173 3 97391", "97391 7 13913", "13913 13913 1" ]
2270162	2 1135081	[ "2270162 2 1135081", "1135081 1135081 1" ]
745994	2 17 37 593	[ "745994 2 372997", "372997 17 21941", "21941 37 593", "593 593 1" ]
264573	3 3 3 41 239	[ "264573 3 88191", "88191 3 29397", "29397 3 9799", "9799 41 239", "239 239 1" ]
2609351	37 109 647	[ "2609351 37 70523", "70523 109 647", "647 647 1" ]
4614801	3 1538267	[ "4614801 3 1538267", "1538267 1538267 1" ]
4281637	17 251861	[ "4281637 17 251861", "251861 251861 1" ]
897295	5 7 31 827	[ "897295 5 179459", "179459 7 25637", "25637 31 827", "827 827 1" ]
2574943	7 367849	[ "2574943 7 367849", "367849 367849 1" ]

140176

2 2 2 2 8761

[ "140176 2 70088", "70088 2 35044", "35044 2 17522", "17522 2 8761", "8761 8761 1" ]

3733348

2 2 19 49123

[ "3733348 2 1866674", "1866674 2 933337", "933337 19 49123", "49123 49123 1" ]

3733611

3 7 177791

[ "3733611 3 1244537", "1244537 7 177791", "177791 177791 1" ]

3014698

2 173 8713

[ "3014698 2 1507349", "1507349 173 8713", "8713 8713 1" ]

1859003

191 9733

[ "1859003 191 9733", "9733 9733 1" ]

2324746

2 1162373

[ "2324746 2 1162373", "1162373 1162373 1" ]

662946

2 3 110491

[ "662946 2 331473", "331473 3 110491", "110491 110491 1" ]

3346546

2 7 19 23 547

[ "3346546 2 1673273", "1673273 7 239039", "239039 19 12581", "12581 23 547", "547 547 1" ]

855774

2 3 3 47543

[ "855774 2 427887", "427887 3 142629", "142629 3 47543", "47543 47543 1" ]

2094601

[ "2094601 2094601 1" ]

4905327

3 7 109 2143

[ "4905327 3 1635109", "1635109 7 233587", "233587 109 2143", "2143 2143 1" ]

1318405

5 11 23971

[ "1318405 5 263681", "263681 11 23971", "23971 23971 1" ]

1721462

2 37 43 541

[ "1721462 2 860731", "860731 37 23263", "23263 43 541", "541 541 1" ]

3013558

2 1506779

[ "3013558 2 1506779", "1506779 1506779 1" ]

4987462

2 19 131249

[ "4987462 2 2493731", "2493731 19 131249", "131249 131249 1" ]

4212626

2 11 419 457

[ "4212626 2 2106313", "2106313 11 191483", "191483 419 457", "457 457 1" ]

1266499

13 97423

[ "1266499 13 97423", "97423 97423 1" ]

3453374

2 53 32579

[ "3453374 2 1726687", "1726687 53 32579", "32579 32579 1" ]

826585

5 165317

[ "826585 5 165317", "165317 165317 1" ]

4459837

823 5419

[ "4459837 823 5419", "5419 5419 1" ]

4886144

2 2 2 2 2 2 2 59 647

[ "4886144 2 2443072", "2443072 2 1221536", "1221536 2 610768", "610768 2 305384", "305384 2 152692", "152692 2 76346", "76346 2 38173", "38173 59 647", "647 647 1" ]

4856120

2 2 2 5 121403

[ "4856120 2 2428060", "2428060 2 1214030", "1214030 2 607015", "607015 5 121403", "121403 121403 1" ]

4815680

2 2 2 2 2 2 5 101 149

[ "4815680 2 2407840", "2407840 2 1203920", "1203920 2 601960", "601960 2 300980", "300980 2 150490", "150490 2 75245", "75245 5 15049", "15049 101 149", "149 149 1" ]

801152

2 2 2 2 2 2 2 11 569

[ "801152 2 400576", "400576 2 200288", "200288 2 100144", "100144 2 50072", "50072 2 25036", "25036 2 12518", "12518 2 6259", "6259 11 569", "569 569 1" ]

4082025

3 5 5 37 1471

[ "4082025 3 1360675", "1360675 5 272135", "272135 5 54427", "54427 37 1471", "1471 1471 1" ]

2865176

2 2 2 43 8329

[ "2865176 2 1432588", "1432588 2 716294", "716294 2 358147", "358147 43 8329", "8329 8329 1" ]

3595773

3 113 10607

[ "3595773 3 1198591", "1198591 113 10607", "10607 10607 1" ]

4239437

1487 2851

[ "4239437 1487 2851", "2851 2851 1" ]

2141028

2 2 3 3 59473

[ "2141028 2 1070514", "1070514 2 535257", "535257 3 178419", "178419 3 59473", "59473 59473 1" ]

940345

5 7 67 401

[ "940345 5 188069", "188069 7 26867", "26867 67 401", "401 401 1" ]

4586833

[ "4586833 4586833 1" ]

2099449

11 17 103 109

[ "2099449 11 190859", "190859 17 11227", "11227 103 109", "109 109 1" ]

3001549

53 56633

[ "3001549 53 56633", "56633 56633 1" ]

4089543

3 251 5431

[ "4089543 3 1363181", "1363181 251 5431", "5431 5431 1" ]

1726915

5 569 607

[ "1726915 5 345383", "345383 569 607", "607 607 1" ]

3295458

2 3 3 3 61027

[ "3295458 2 1647729", "1647729 3 549243", "549243 3 183081", "183081 3 61027", "61027 61027 1" ]

3593387

7 513341

[ "3593387 7 513341", "513341 513341 1" ]

2700532

2 2 675133

[ "2700532 2 1350266", "1350266 2 675133", "675133 675133 1" ]

4079724

2 2 3 11 31 997

[ "4079724 2 2039862", "2039862 2 1019931", "1019931 3 339977", "339977 11 30907", "30907 31 997", "997 997 1" ]

264619

[ "264619 264619 1" ]

4378755

3 5 47 6211

[ "4378755 3 1459585", "1459585 5 291917", "291917 47 6211", "6211 6211 1" ]

927592

2 2 2 47 2467

[ "927592 2 463796", "463796 2 231898", "231898 2 115949", "115949 47 2467", "2467 2467 1" ]

660545

5 132109

[ "660545 5 132109", "132109 132109 1" ]

4101418

2 211 9719

[ "4101418 2 2050709", "2050709 211 9719", "9719 9719 1" ]

2147965

5 269 1597

[ "2147965 5 429593", "429593 269 1597", "1597 1597 1" ]

2711596

2 2 79 8581

[ "2711596 2 1355798", "1355798 2 677899", "677899 79 8581", "8581 8581 1" ]

2026106

2 1013053

[ "2026106 2 1013053", "1013053 1013053 1" ]

3849218

2 107 17987

[ "3849218 2 1924609", "1924609 107 17987", "17987 17987 1" ]

1169540

2 2 5 58477

[ "1169540 2 584770", "584770 2 292385", "292385 5 58477", "58477 58477 1" ]

1986011

541 3671

[ "1986011 541 3671", "3671 3671 1" ]

4241299

109 167 233

[ "4241299 109 38911", "38911 167 233", "233 233 1" ]

4554418

2 11 241 859

[ "4554418 2 2277209", "2277209 11 207019", "207019 241 859", "859 859 1" ]

2957577

3 7 140837

[ "2957577 3 985859", "985859 7 140837", "140837 140837 1" ]

4600887

3 1533629

[ "4600887 3 1533629", "1533629 1533629 1" ]

2901054

2 3 13 13 2861

[ "2901054 2 1450527", "1450527 3 483509", "483509 13 37193", "37193 13 2861", "2861 2861 1" ]

2260145

5 19 37 643

[ "2260145 5 452029", "452029 19 23791", "23791 37 643", "643 643 1" ]

239287

[ "239287 239287 1" ]

3630974

2 29 62603

[ "3630974 2 1815487", "1815487 29 62603", "62603 62603 1" ]

2763098

2 13 106273

[ "2763098 2 1381549", "1381549 13 106273", "106273 106273 1" ]

4050534

2 3 19 35531

[ "4050534 2 2025267", "2025267 3 675089", "675089 19 35531", "35531 35531 1" ]

1587306

2 3 7 7 5399

[ "1587306 2 793653", "793653 3 264551", "264551 7 37793", "37793 7 5399", "5399 5399 1" ]

689317

[ "689317 689317 1" ]

1141760

2 2 2 2 2 2 2 2 2 2 5 223

[ "1141760 2 570880", "570880 2 285440", "285440 2 142720", "142720 2 71360", "71360 2 35680", "35680 2 17840", "17840 2 8920", "8920 2 4460", "4460 2 2230", "2230 2 1115", "1115 5 223", "223 223 1" ]

1685908

2 2 7 19 3169

[ "1685908 2 842954", "842954 2 421477", "421477 7 60211", "60211 19 3169", "3169 3169 1" ]

4561331

[ "4561331 4561331 1" ]

4697642

2 173 13577

[ "4697642 2 2348821", "2348821 173 13577", "13577 13577 1" ]

2929199

7 13 32189

[ "2929199 7 418457", "418457 13 32189", "32189 32189 1" ]

3698259

3 367 3359

[ "3698259 3 1232753", "1232753 367 3359", "3359 3359 1" ]

4667878

2 2333939

[ "4667878 2 2333939", "2333939 2333939 1" ]

3934553

7 7 7 11471

[ "3934553 7 562079", "562079 7 80297", "80297 7 11471", "11471 11471 1" ]

4735380

2 2 3 5 13 13 467

[ "4735380 2 2367690", "2367690 2 1183845", "1183845 3 394615", "394615 5 78923", "78923 13 6071", "6071 13 467", "467 467 1" ]

438701

[ "438701 438701 1" ]

3106076

2 2 31 37 677

[ "3106076 2 1553038", "1553038 2 776519", "776519 31 25049", "25049 37 677", "677 677 1" ]

3633653

[ "3633653 3633653 1" ]

1538998

2 373 2063

[ "1538998 2 769499", "769499 373 2063", "2063 2063 1" ]

1784759

541 3299

[ "1784759 541 3299", "3299 3299 1" ]

3036723

3 1012241

[ "3036723 3 1012241", "1012241 1012241 1" ]

2274413

17 337 397

[ "2274413 17 133789", "133789 337 397", "397 397 1" ]

952632

2 2 2 3 3 101 131

[ "952632 2 476316", "476316 2 238158", "238158 2 119079", "119079 3 39693", "39693 3 13231", "13231 101 131", "131 131 1" ]

4103433

3 3 3 379 401

[ "4103433 3 1367811", "1367811 3 455937", "455937 3 151979", "151979 379 401", "401 401 1" ]

4550591

[ "4550591 4550591 1" ]

3583364

2 2 895841

[ "3583364 2 1791682", "1791682 2 895841", "895841 895841 1" ]

2857509

3 3 79 4019

[ "2857509 3 952503", "952503 3 317501", "317501 79 4019", "4019 4019 1" ]

1598553

3 3 11 67 241

[ "1598553 3 532851", "532851 3 177617", "177617 11 16147", "16147 67 241", "241 241 1" ]

4625699

13 13 101 271

[ "4625699 13 355823", "355823 13 27371", "27371 101 271", "271 271 1" ]

1032942

2 3 172157

[ "1032942 2 516471", "516471 3 172157", "172157 172157 1" ]

3651113

139 26267

[ "3651113 139 26267", "26267 26267 1" ]

559971

3 3 62219

[ "559971 3 186657", "186657 3 62219", "62219 62219 1" ]

2095546

2 1047773

[ "2095546 2 1047773", "1047773 1047773 1" ]

954825

3 5 5 29 439

[ "954825 3 318275", "318275 5 63655", "63655 5 12731", "12731 29 439", "439 439 1" ]

253553

[ "253553 253553 1" ]

1753038

2 3 3 7 13913

[ "1753038 2 876519", "876519 3 292173", "292173 3 97391", "97391 7 13913", "13913 13913 1" ]

2270162

2 1135081

[ "2270162 2 1135081", "1135081 1135081 1" ]

745994

2 17 37 593

[ "745994 2 372997", "372997 17 21941", "21941 37 593", "593 593 1" ]

264573

3 3 3 41 239

[ "264573 3 88191", "88191 3 29397", "29397 3 9799", "9799 41 239", "239 239 1" ]

2609351

37 109 647

[ "2609351 37 70523", "70523 109 647", "647 647 1" ]

4614801

3 1538267

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4281637

17 251861

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897295

5 7 31 827

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2574943

7 367849

[ "2574943 7 367849", "367849 367849 1" ]