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# How do you find the greatest common factor of 30135 using prime factorization?

Updated: 4/28/2022

Wiki User

14y ago

You do not. To have a greatest common factor, you need two or more numbers. A common factor is a factor that two or more number have in common.

However, the prime factorization of all the numbers will help you find the greatest common factor. The greatest common factor will be the prime factors they have in common multiplied together.

Example:

The prime factorization of 30135 is 3 x 5 x 7 x 7 x 41.

The prime factorization of 98 is 2 x 7 x 7.

The prime factors they have in common are 7 and 7, so the greatest common factor is 7 x 7 = 49.

Wiki User

14y ago
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### What are the first 1000 triangular numbers?

This is quite clearly a trollish question. However I will oblige said troll: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431, 1485, 1540, 1596, 1653, 1711, 1770, 1830, 1891, 1953, 2016, 2080, 2145, 2211, 2278, 2346, 2415, 2485, 2556, 2628, 2701, 2775, 2850, 2926, 3003, 3081, 3160, 3240, 3321, 3403, 3486, 3570, 3655, 3741, 3828, 3916, 4005, 4095, 4186, 4278, 4371, 4465, 4560, 4656, 4753, 4851, 4950, 5050, 5151, 5253, 5356, 5460, 5565, 5671, 5778, 5886, 5995, 6105, 6216, 6328, 6441, 6555, 6670, 6786, 6903, 7021, 7140, 7260, 7381, 7503, 7626, 7750, 7875, 8001, 8128, 8256, 8385, 8515, 8646, 8778, 8911, 9045, 9180, 9316, 9453, 9591, 9730, 9870, 10011, 10153, 10296, 10440, 10585, 10731, 10878, 11026, 11175, 11325, 11476, 11628, 11781, 11935, 12090, 12246, 12403, 12561, 12720, 12880, 13041, 13203, 13366, 13530, 13695, 13861, 14028, 14196, 14365, 14535, 14706, 14878, 15051, 15225, 15400, 15576, 15753, 15931, 16110, 16290, 16471, 16653, 16836, 17020, 17205, 17391, 17578, 17766, 17955, 18145, 18336, 18528, 18721, 18915, 19110, 19306, 19503, 19701, 19900, 20100, 20301, 20503, 20706, 20910, 21115, 21321, 21528, 21736, 21945, 22155, 22366, 22578, 22791, 23005, 23220, 23436, 23653, 23871, 24090 ,24310, 24531, 24753, 24976, 25200, 25425, 25651, 25878, 26106, 26335, 26565, 26796, 27028, 27261, 27495, 27730, 27966, 28203, 28441, 28680, 28920, 29161, 29403, 29646, 29890, 30135, 30381, 30628, 30876, 31125, 31375, 31626, 31878, 32131, 32385, 32640, 32896, 33153, 33411, 33670, 33930, 34191, 34453, 34716, 34980, 35245, 35511, 35778, 36046, 36315, 36585, 36856, 37128, 37401, 37675, 37950, 38226, 38503, 38781, 39060, 39340, 39621, 39903, 40186, 40470, 40755, 41041, 41328, 41616, 41905, 42195, 42486, 42778, 43071, 43365, 43660, 43956, 44253, 44551, 44850, 45150, 45451, 45753, 46056, 46360, 46665, 46971, 47278, 47586, 47895, 48205, 48516, 48828, 49141, 49455, 49770, 50086, 50403, 50721, 51040, 51360, 51681, 52003, 52326, 52650, 52975, 53301, 53628, 53956, 54285, 54615, 54946, 55278, 55611, 55945, 56280, 56616, 56953, 57291, 57630, 57970, 58311, 58653, 58996, 59340, 59685, 60031, 60378, 60726, 61075, 61425, 61776, 62128, 62481, 62835, 63190, 63546, 63903, 64261, 64620, 64980, 65341, 65703, 66066, 66430, 66795, 67161, 67528, 67896, 68265, 68635, 69006, 69378, 69751, 70125, 70500, 70876, 71253, 71631, 72010, 72390, 72771, 73153, 73536, 73920, 74305, 74691, 75078, 75466, 75855, 76245, 76636, 77028, 77421, 77815, 78210, 78606, 79003, 79401, 79800, 80200, 80601, 81003, 81406, 81810, 82215, 82621, 83028, 83436, 83845, 84255, 84666, 85078, 85491, 85905, 86320, 86736, 87153, 87571, 87990, 88410, 88831, 89253, 89676, 90100, 90525, 90951, 91378, 91806, 92235, 92665, 93096, 93528, 93961, 94395, 94830, 95266, 95703, 96141, 96580, 97020, 97461, 97903, 98346, 98790, 99235, 99681, 100128, 100576, 101025, 101475, 101926, 102378, 102831, 103285, 103740, 104196, 104653, 105111, 105570, 106030, 106491, 106953, 107416, 107880, 108345, 108811, 109278, 109746, 110215, 110685, 111156, 111628, 112101, 112575, 113050, 113526, 114003, 114481, 114960, 115440, 115921, 116403, 116886, 117370, 117855, 118341, 118828, 119316, 119805, 120295, 120786 ,121278, 121771, 122265, 122760, 123256, 123753, 124251, 124750, 125250, 125751, 126253, 126756, 127260, 127765, 128271, 128778, 129286, 129795, 130305, 130816, 131328, 131841, 132355, 132870, 133386, 133903, 134421, 134940, 135460, 135981, 136503, 137026, 137550, 138075, 138601, 139128, 139656, 140185, 140715, 141246, 141778, 142311, 142845, 143380, 143916, 144453, 144991, 145530, 146070 ,146611, 147153, 147696, 148240, 148785, 149331, 149878, 150426, 150975, 151525, 152076, 152628, 153181, 153735, 154290, 154846, 155403, 155961,156520, 157080, 157641, 158203, 158766, 159330, 159895, 160461, 161028, 161596, 162165, 162735, 163306, 163878, 164451, 165025, 165600, 166176, 166753, 167331, 167910, 168490, 169071, 169653, 170236, 170820, 171405, 171991, 172578, 173166, 173755, 174345, 174936, 175528, 176121, 176715, 177310, 177906, 178503, 179101, 179700, 180300, 180901, 181503, 182106, 182710, 183315, 183921, 184528, 185136, 185745, 186355, 186966, 187578, 188191, 188805, 189420, 190036, 190653, 191271, 191890, 192510, 193131, 193753, 194376, 195000, 195625, 196251, 196878, 197506, 198135, 198765, 199396, 200028, 200661, 201295, 201930, 202566, 203203, 203841, 204480, 205120, 205761, 206403, 207046, 207690, 208335, 208981, 209628, 210276, 210925, 211575, 212226, 212878, 213531, 214185, 214840, 215496, 216153, 216811, 217470, 218130, 218791, 219453, 220116, 220780, 221445, 222111, 222778, 223446, 224115, 224785, 225456, 226128, 226801, 227475, 228150, 228826, 229503, 230181, 230860, 231540, 232221, 232903, 233586, 234270, 234955, 235641, 236328, 237016, 237705, 238395, 239086, 239778, 240471, 241165, 241860, 242556, 243253, 243951, 244650, 245350, 246051, 246753, 247456, 248160, 248865, 249571, 250278, 250986, 251695, 252405, 253116, 253828, 254541, 255255, 255970, 256686, 257403, 258121, 258840, 259560, 260281, 261003, 261726, 262450, 263175, 263901, 264628, 265356, 266085, 266815, 267546, 268278, 269011, 269745, 270480, 271216, 271953, 272691, 273430, 274170, 274911, 275653, 276396, 277140, 277885, 278631, 279378, 280126, 280875, 281625, 282376, 283128, 283881, 284635, 285390, 286146, 286903, 287661, 288420, 289180, 289941, 290703, 291466, 292230, 292995, 293761, 294528, 295296, 296065, 296835, 297606, 298378, 299151, 299925, 300700, 301476, 302253, 303031, 303810, 304590, 305371, 306153, 306936, 307720, 308505, 309291, 310078, 310866, 311655, 312445, 313236, 314028, 314821, 315615, 316410, 317206, 318003, 318801, 319600, 320400, 321201, 322003, 322806, 323610, 324415, 325221, 326028, 326836, 327645, 328455, 329266, 330078, 330891, 331705, 332520, 333336, 334153, 334971, 335790, 336610, 337431, 338253, 339076, 339900, 340725, 341551, 342378, 343206, 344035, 344865, 345696, 346528, 347361, 348195, 349030, 349866, 350703, 351541, 352380, 353220, 354061, 354903, 355746, 356590, 357435, 358281, 359128, 359976, 360825, 361675, 362526, 363378, 364231, 365085, 365940, 366796, 367653, 368511, 369370, 370230, 371091, 371953, 372816, 373680, 374545, 375411, 376278, 377146, 378015, 378885, 379756, 380628, 381501, 382375, 383250, 384126, 385003, 385881, 386760, 387640, 388521, 389403, 390286, 391170, 392055, 392941, 393828, 394716, 395605, 396495, 397386, 398278, 399171, 400065, 400960, 401856, 402753, 403651, 404550, 405450, 406351, 407253, 408156, 409060, 409965, 410871, 411778, 412686, 413595, 414505, 415416, 416328, 417241, 418155, 419070, 419986, 420903, 421821, 422740, 423660, 424581, 425503, 426426, 427350, 428275, 429201, 430128, 431056, 431985, 432915, 433846, 434778, 435711, 436645, 437580, 438516, 439453, 440391, 441330, 442270, 443211, 444153, 445096, 446040, 446985, 447931, 448878, 449826, 450775, 451725, 452676, 453628, 454581, 455535, 456490, 457446, 458403, 459361, 460320, 461280, 462241, 463203, 464166, 465130, 466095, 467061, 468028, 468996, 469965, 470935, 471906, 472878, 473851, 474825, 475800, 476776, 477753, 478731, 479710, 480690, 481671, 482653, 483636, 484620, 485605, 486591, 487578, 488566, 489555, 490545, 491536, 492528, 493521, 494515, 495510, 496506, 497503, 498501, 499500, 500500, ...you didn't think I'd do it, did you...

### What are all of the multiple of 35?

The first 1000 multiples of 35 are: 35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455, 490, 525, 560, 595, 630, 665, 700, 735, 770, 805, 840, 875, 910, 945, 980, 1015, 1050, 1085, 1120, 1155, 1190, 1225, 1260, 1295, 1330, 1365, 1400, 1435, 1470, 1505, 1540, 1575, 1610, 1645, 1680, 1715, 1750, 1785, 1820, 1855, 1890, 1925, 1960, 1995, 2030, 2065, 2100, 2135, 2170, 2205, 2240, 2275, 2310, 2345, 2380, 2415, 2450, 2485, 2520, 2555, 2590, 2625, 2660, 2695, 2730, 2765, 2800, 2835, 2870, 2905, 2940, 2975, 3010, 3045, 3080, 3115, 3150, 3185, 3220, 3255, 3290, 3325, 3360, 3395, 3430, 3465, 3500, 3535, 3570, 3605, 3640, 3675, 3710, 3745, 3780, 3815, 3850, 3885, 3920, 3955, 3990, 4025, 4060, 4095, 4130, 4165, 4200, 4235, 4270, 4305, 4340, 4375, 4410, 4445, 4480, 4515, 4550, 4585, 4620, 4655, 4690, 4725, 4760, 4795, 4830, 4865, 4900, 4935, 4970, 5005, 5040, 5075, 5110, 5145, 5180, 5215, 5250, 5285, 5320, 5355, 5390, 5425, 5460, 5495, 5530, 5565, 5600, 5635, 5670, 5705, 5740, 5775, 5810, 5845, 5880, 5915, 5950, 5985, 6020, 6055, 6090, 6125, 6160, 6195, 6230, 6265, 6300, 6335, 6370, 6405, 6440, 6475, 6510, 6545, 6580, 6615, 6650, 6685, 6720, 6755, 6790, 6825, 6860, 6895, 6930, 6965, 7000, 7035, 7070, 7105, 7140, 7175, 7210, 7245, 7280, 7315, 7350, 7385, 7420, 7455, 7490, 7525, 7560, 7595, 7630, 7665, 7700, 7735, 7770, 7805, 7840, 7875, 7910, 7945, 7980, 8015, 8050, 8085, 8120, 8155, 8190, 8225, 8260, 8295, 8330, 8365, 8400, 8435, 8470, 8505, 8540, 8575, 8610, 8645, 8680, 8715, 8750, 8785, 8820, 8855, 8890, 8925, 8960, 8995, 9030, 9065, 9100, 9135, 9170, 9205, 9240, 9275, 9310, 9345, 9380, 9415, 9450, 9485, 9520, 9555, 9590, 9625, 9660, 9695, 9730, 9765, 9800, 9835, 9870, 9905, 9940, 9975, 10010, 10045, 10080, 10115, 10150, 10185, 10220, 10255, 10290, 10325, 10360, 10395, 10430, 10465, 10500, 10535, 10570, 10605, 10640, 10675, 10710, 10745, 10780, 10815, 10850, 10885, 10920, 10955, 10990, 11025, 11060, 11095, 11130, 11165, 11200, 11235, 11270, 11305, 11340, 11375, 11410, 11445, 11480, 11515, 11550, 11585, 11620, 11655, 11690, 11725, 11760, 11795, 11830, 11865, 11900, 11935, 11970, 12005, 12040, 12075, 12110, 12145, 12180, 12215, 12250, 12285, 12320, 12355, 12390, 12425, 12460, 12495, 12530, 12565, 12600, 12635, 12670, 12705, 12740, 12775, 12810, 12845, 12880, 12915, 12950, 12985, 13020, 13055, 13090, 13125, 13160, 13195, 13230, 13265, 13300, 13335, 13370, 13405, 13440, 13475, 13510, 13545, 13580, 13615, 13650, 13685, 13720, 13755, 13790, 13825, 13860, 13895, 13930, 13965, 14000, 14035, 14070, 14105, 14140, 14175, 14210, 14245, 14280, 14315, 14350, 14385, 14420, 14455, 14490, 14525, 14560, 14595, 14630, 14665, 14700, 14735, 14770, 14805, 14840, 14875, 14910, 14945, 14980, 15015, 15050, 15085, 15120, 15155, 15190, 15225, 15260, 15295, 15330, 15365, 15400, 15435, 15470, 15505, 15540, 15575, 15610, 15645, 15680, 15715, 15750, 15785, 15820, 15855, 15890, 15925, 15960, 15995, 16030, 16065, 16100, 16135, 16170, 16205, 16240, 16275, 16310, 16345, 16380, 16415, 16450, 16485, 16520, 16555, 16590, 16625, 16660, 16695, 16730, 16765, 16800, 16835, 16870, 16905, 16940, 16975, 17010, 17045, 17080, 17115, 17150, 17185, 17220, 17255, 17290, 17325, 17360, 17395, 17430, 17465, 17500, 17535, 17570, 17605, 17640, 17675, 17710, 17745, 17780, 17815, 17850, 17885, 17920, 17955, 17990, 18025, 18060, 18095, 18130, 18165, 18200, 18235, 18270, 18305, 18340, 18375, 18410, 18445, 18480, 18515, 18550, 18585, 18620, 18655, 18690, 18725, 18760, 18795, 18830, 18865, 18900, 18935, 18970, 19005, 19040, 19075, 19110, 19145, 19180, 19215, 19250, 19285, 19320, 19355, 19390, 19425, 19460, 19495, 19530, 19565, 19600, 19635, 19670, 19705, 19740, 19775, 19810, 19845, 19880, 19915, 19950, 19985, 20020, 20055, 20090, 20125, 20160, 20195, 20230, 20265, 20300, 20335, 20370, 20405, 20440, 20475, 20510, 20545, 20580, 20615, 20650, 20685, 20720, 20755, 20790, 20825, 20860, 20895, 20930, 20965, 21000, 21035, 21070, 21105, 21140, 21175, 21210, 21245, 21280, 21315, 21350, 21385, 21420, 21455, 21490, 21525, 21560, 21595, 21630, 21665, 21700, 21735, 21770, 21805, 21840, 21875, 21910, 21945, 21980, 22015, 22050, 22085, 22120, 22155, 22190, 22225, 22260, 22295, 22330, 22365, 22400, 22435, 22470, 22505, 22540, 22575, 22610, 22645, 22680, 22715, 22750, 22785, 22820, 22855, 22890, 22925, 22960, 22995, 23030, 23065, 23100, 23135, 23170, 23205, 23240, 23275, 23310, 23345, 23380, 23415, 23450, 23485, 23520, 23555, 23590, 23625, 23660, 23695, 23730, 23765, 23800, 23835, 23870, 23905, 23940, 23975, 24010, 24045, 24080, 24115, 24150, 24185, 24220, 24255, 24290, 24325, 24360, 24395, 24430, 24465, 24500, 24535, 24570, 24605, 24640, 24675, 24710, 24745, 24780, 24815, 24850, 24885, 24920, 24955, 24990, 25025, 25060, 25095, 25130, 25165, 25200, 25235, 25270, 25305, 25340, 25375, 25410, 25445, 25480, 25515, 25550, 25585, 25620, 25655, 25690, 25725, 25760, 25795, 25830, 25865, 25900, 25935, 25970, 26005, 26040, 26075, 26110, 26145, 26180, 26215, 26250, 26285, 26320, 26355, 26390, 26425, 26460, 26495, 26530, 26565, 26600, 26635, 26670, 26705, 26740, 26775, 26810, 26845, 26880, 26915, 26950, 26985, 27020, 27055, 27090, 27125, 27160, 27195, 27230, 27265, 27300, 27335, 27370, 27405, 27440, 27475, 27510, 27545, 27580, 27615, 27650, 27685, 27720, 27755, 27790, 27825, 27860, 27895, 27930, 27965, 28000, 28035, 28070, 28105, 28140, 28175, 28210, 28245, 28280, 28315, 28350, 28385, 28420, 28455, 28490, 28525, 28560, 28595, 28630, 28665, 28700, 28735, 28770, 28805, 28840, 28875, 28910, 28945, 28980, 29015, 29050, 29085, 29120, 29155, 29190, 29225, 29260, 29295, 29330, 29365, 29400, 29435, 29470, 29505, 29540, 29575, 29610, 29645, 29680, 29715, 29750, 29785, 29820, 29855, 29890, 29925, 29960, 29995, 30030, 30065, 30100, 30135, 30170, 30205, 30240, 30275, 30310, 30345, 30380, 30415, 30450, 30485, 30520, 30555, 30590, 30625, 30660, 30695, 30730, 30765, 30800, 30835, 30870, 30905, 30940, 30975, 31010, 31045, 31080, 31115, 31150, 31185, 31220, 31255, 31290, 31325, 31360, 31395, 31430, 31465, 31500, 31535, 31570, 31605, 31640, 31675, 31710, 31745, 31780, 31815, 31850, 31885, 31920, 31955, 31990, 32025, 32060, 32095, 32130, 32165, 32200, 32235, 32270, 32305, 32340, 32375, 32410, 32445, 32480, 32515, 32550, 32585, 32620, 32655, 32690, 32725, 32760, 32795, 32830, 32865, 32900, 32935, 32970, 33005, 33040, 33075, 33110, 33145, 33180, 33215, 33250, 33285, 33320, 33355, 33390, 33425, 33460, 33495, 33530, 33565, 33600, 33635, 33670, 33705, 33740, 33775, 33810, 33845, 33880, 33915, 33950, 33985, 34020, 34055, 34090, 34125, 34160, 34195, 34230, 34265, 34300, 34335, 34370, 34405, 34440, 34475, 34510, 34545, 34580, 34615, 34650, 34685, 34720, 34755, 34790, 34825, 34860, 34895, 34930, 34965, 35000 If you want any more (the 1001th multiple onwards - there is no upper limit to the multiples of 35) you'll have to work them out yourself.