what are the factors of 37, 51, and 45?

Question

i just dont get it

Answer 1

37 is prime, so it's only factors are 1 and 37
51 has factors of 1,51 and 3,17
45 has factors of 1,45 ; 3,15 and 5,9

the greatest common factor of the 3 digits is 1, which makes them relatively prime

the factors are the numbers that you can multiply together to get the product

Answer 2

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Here are the first values of G G(2) = 8 8 = 2*4 9 = 3*3 G(3) = 14 14 = 2*7, 15 = 3*5, 16 = 4*4. G(4) = 24 24 = 4*6, 25 = 5*5, 26 = 2*13, 27 = 3*9 G(5) = 24 24 = 3*8, 25 = 5*5, 26 = 2*13, 27 = 3*9, 28 = 4*7 G(6) = G(7 ) = 90 90 = 9 * 10, 91 = 7*13, 92 = 4*23, 93 = 3*31, 94 = 2*47, 95 = 5*19, 96 = 6*16 G(8) = 114 114 = 3*38, 115 = 5*23 116 = 4*29, 117 = 9*13, 118 = 2*59, 119 = 7*17 120 = 6*20, 121 = 11^2 G(9) = 182 182 = 2*91, 183 = 3*61, 184 = 8*23, 185 = 5*37, 186 = 6*31, 187 = 11*17, 188 = 4*47, 189 = 9*21, 190 = 10*19 G(10) = G(11) = 510 510 = 10*51, 511 = 7*73, 512 = 16*32, 513 = 9*57, 514 = 2*257, 515 = 5*103, 516 = 6*86, 517 = 11*47, 518 = 14*37, 519 = 3*173, 520 = 20*26. G(12) = G(13) = G(14) = 524 524 = 4*131, 525 = 25*21, 526 = 2*263, 527 = 17*31, 528 = 16*33, 529 = 23*23 530 = 10*53, 531 = 9*59, 532 = 28*19, 533 = 13*41, 534 = 6*89, 535 = 5*107, 536 = 8*67, 537 = 3*179 @ smci, it seems early. I started this since it is the only way to get a feeling, but before G(25) or more, I doubt we'll get an informed idea. G(15) = G(16) = G(17) = 1260 1260 = 20*63, 1261 = 13*97, 1262 = 2*631,1263 = 3*421, 1264 = 16*79, 1265 = 5*253, 1266 = 6*211, 1267 = 7*181, 1268 = 4*317, 1269 = 27*47, 1270 = 10*127, 1271 = 31*41, 1272 = 24*53, 1273 = 19*67, 1274 = 26*49, 1275 = 25*51, 1276 = 29*44 G(18) = G(19) = 1332 1332 = 36*37, 1333 = 31*43, 1334 = 29*46, 1335 = 15*89 1336 = 8*167, 1337 = 7*191, 1338 = 6*223, 1339 = 13*103, 1340 = 20*67, 1341 = 9*149, 1342 = 22*61, 1343 = 17*79, 1344 = 21*64, 1345 = 5*269, 1346 = 2*673, 1347 = 3*449, 1348 = 4*337, 1349 = 19*71, 1350 = 10*135. G(20) = G(21) = 2312 2312 = 34*68, 2313 = 9*257, 2314 = 26*89, 2315 = 5*463, 2316 = 12*193, 2317 = 7*331, 2318 = 38*61, 2319 = 3*773, 2320 = 20*116, 2321 = 11*211, 2322 = 43*54, 2323 = 23*101 2324 = 28*83, 2325 = 25*93, 2326 = 2*1163, 2327 = 13*179, 2328 = 24*97, 2329 = 17*137, 2330 = 10*233, 2331 = 37*63, 2332 = 44*53 G(22) = 4179 4179 = 21*199, 4180 = 20*209, 4181 = 37*113, 4182 = 41*102, 4183 = 47*89, 4184 = 8*523, 4185 = 31*135, 4186 = 23*182, 4187 = 53*79, 4188 = 12*349, 4189 = 59*71, 4190 = 10*419, 4191 = 33*127, 4192 = 32*131, 4193 = 7 *599, 4194 = 18*233, 4195 = 5*839, 4196 = 4*1049, 4197 = 3*1399, 4198 = 2*2099, 4199 = 19*221, 4200 = 42*100. G(23) = G(24) = G(25) = 5122 5122 = 26*197, 5123 = 47*109, 5124 = 28*183, 5125 = 41*125, 5126 = 22*233, 5127 = 3*1709, 5128 = 8*641, 5129 = 23*223, 5130 = 10*513, 5131 = 7*733, 5132 = 4*1283, 5133 = 59*87, 5134 = 17*302, 5135 = 65*79, 5136 = 48*107, 5137 = 11*467, 5138 = 14*367, 5139 = 9*571, 5140 = 20*257, 5141 = 53*97, 5142 = 6*857, 5143 = 37*139, 5144 = 2*2572, 5145 = 49*105, 5146 = 62*83 In line with the initial inspiration of the question, one should reach G(33) before risking any guestimate. G(26) = G(27) = 8972 8972 = 4*2243, 8973 = 9*997, 8974 = 14*641, 8975 = 25*359, 8976 = 48*187, 8977 = 47*191, 8978 = 67*134, 8979 = 41*219, 8980 = 20*449, 8981 = 7*1283, 8982 = 18*499, 8983 = 13*691, 8984 = 8*1123, 8985 = 15*599, 8986 = 2*4493, 8987 = 43*209, 8988 = 42*214, 8989 = 89*101, 8990 = 31*290, 8991 = 37*243, 8992 = 32*281, 8993 = 23*391, 8994 = 6*1499, 8995 = 35*257, 8996 = 51*173, 8997 = 2*2999, 8998 = 22*409 G(28) = G(29) = G(30) = 16144 16144 = 16*1009, 16145 = 5*3229, 16146 = 54*299, 16147 = 67*241, 16148 = 44*367, 16149 = 21*769, 16150 = 50*323, 16151 = 31*521, 16152 = 24*673, 16153 = 29*557, 16154 = 82*197, 16155 = 45*359, 16156 = 28*577, 16157 = 107*151, 16158 = 6*2693, 16159 = 113*143, 16160 = 20*808, 16161 = 3*5387, 16162 = 2*8081, 16163 = 7*2309, 16164 = 36*449, 16165 = 61*265, 16166 = 118*137, 16167 = 51*317, 16168 = 47*344, 16169 = 37*437, 16170 = 10*1617, 16171 = 103*157, 16172 = 52*311, 16173 = 27*599 G(31) = G(32) = 17259 17259 = 33*523, 17260 = 20*863, 17261 = 41*421, 17262 = 126*137, 17263 = 61*283, 17264 = 52*332, 17265 = 15*1151, 17266 = 97*178, 17267 = 31*557, 17268 = 12*1439, 17269 = 7*2467, 17270 = 10*1727, 17271 = 101*171, 17272 = 127*136, 17273 = 23*751, 17274 = 6*2879, 17275 = 25*691, 17276 = 28*617, 17277 = 39*443, 17278 = 106*163, 17279 = 37*467, 17280 = 120*144, 17281 = 11*1571, 17282 = 2*8641, 17283 = 21*823, 17284 = 116*149, 17285 = 5*3457, 17286 = 67*258, 17287 = 59*293, 17288 = 8*2131, 17289 = 17*1017, 17290 = 70*247 G(33) = G(34) = G(35) = G(36) = G(37) = 20810 20810 = 10*2081, 20811 = 21*991, 20812 = 43*484, 20813 = 13*1601, 20814 = 6*3469, 20815 = 115*181, 20816 = 16*1301, 20817 = 81*257, 20818 = 14*1487, 20819 = 109*191, 20820 = 60*347, 20821 = 47*443, 20822 = 58*359, 20823 = 33*631, 20824 = 137*152, 20825 = 49*425, 20826 = 89*234, 20827 = 59*353, 20828 = 127*164, 20829 = 131*159, 20830 = 5*4166, 20831 = 37*563, 20832 = 96*217, 20833 = 83*251, 20834 = 22*947, 20835 = 45*463, 20836 = 4*5209, 20837 = 67*311, 20838 = 138*151, 20839 = 91*229, 20840 = 40*521, 20841 = 3*6947, 20842 = 34*613, 20843 = 19*1097, 20844 = 108*193, 20845 = 55*379, 20846 = 7*2978 Edit Somme very rough estimates suggest that (ln(G(n)))^2 / (n* ln n) should be of the order of 1. For 8,13,18,23,28,33 we get 1.34, 1.17, 0.99, 1.01,1.006, 0.85 . So H(n) = exp( sqrt( n*ln n) ) is a reasonable estimator for G(n), though hopefully conservative. Otherwise it would mean that we have to wait till 127000 to find G(38). edit: another similar candidate would be K(n) = exp(sqrt(ln n!) ) K(37) = 21300 to be compared with G(37) = 20810. Note that K(38) = 25522. Edit: wrong again! G(38) = ....... = G(53) = 31399 It is enough to check that for all numbers k less than 53/2, there is at most one number of the form k*p in that interval. Indeed all these numbers will have different factors in their decompositions. If 2 numbers have a factor larger than 53/2 in common, they must be consecutive multiples kn, k(n+1), so one of them will be a multiple of 2k; In the end all numbers have their own factors which they share with no other. Let's just list those factors, and the corresponding number. For the product only the 2 last digits are given, the numbers being between 31399 and 31451. 3*10477 = ...31, 4*7853 = ...12, 5*6287 = ...35, 6*5237 = ...22, 7*4493 = ...51, 8*3929 = ...32, 8*3931 = ...48 which can be written as 2*15724 since factor 2 is free., 9*3491 = ...19, 11* 2857 = ...27, 12*2617 = ...04, 13*2417 = ...21, 14*2243 = ...02, 17*1847 = 31399, 18*1747 = ...46, 20*1571 = ...20, 22*1429 = ...38, 23*1361 = ...03. Edit: G(54) = 302343 - - - 302396 2*151189 = ...78, 3*100787 = 61, 8*37799 = ...92, 9*33599 = ...91, 11*27487 = ...57, 16*18899 = ...84, 19*15913 = ...47, 23*13147 = ...81 Note that the ratio ( ln G(54) )^2 / ( 54 * ln(54) ) = 0.73929 and that ( ln G(38) )^2 / ( 38 * ln(38) ) = 0.77564. Also K(54) = exp(sqrt( ln(54!) ) = 369069.652....

Answer 3

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RE:
what are the factors of 37, 51, and 45?
i just dont get it

Answer 4

37= 1,37
51=1,3,17,51
45=1,3,5,9,15,45