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Édition du: 12/04/2024 |
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INDEX |
Forme retournées |
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Produits & Retournés
Multiplication
qui reste exacte en prenant les retournés à la fois des facteurs et du
produit. |
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Sommaire de cette page >>> Approche >>> Exemples |
Débutants Glossaire |
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Observation Soit le produit de deux nombres de deux chiffres
et le produit de ces deux nombres retournés. Les deux produits sont l'un le retourné de
l'autre. Est-ce toujours vrai ? Presque … |
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Calcul littéral La forme générique d'un nombre de deux chiffres
est n = 10a + b. On développe le calcul du produit des nombres et
le calcul des nombres retournés. Le produit des retournés est exactement le retourné
du produit des nombres. |
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Attention Nous sommes en décimal. Pour garantir l'identité,
il est nécessaire que les chiffres qui vont prendre la place des centaines, des
dizaines et des unités ne dépassent pas 9. Autrement-dit, il ne faut pas de retenues. Cas particulier pour une multiplication entre
repdigits (ex: 77 × 88 = 6776 qui est réversible) |
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Deux chiffres de 10 à 99 11, 12, 132, 231, 21, 11 11, 13, 143, 341, 31, 11 11, 14, 154, 451, 41, 11 11, 15, 165, 561, 51, 11 11, 16, 176, 671, 61, 11 11, 17, 187, 781, 71, 11 11, 18, 198, 891, 81, 11 11, 21, 231, 132, 12, 11 11, 22, 242, 242, 22, 11 11, 23, 253, 352, 32, 11 11, 24, 264, 462, 42, 11 11, 25, 275, 572, 52, 11 11, 26, 286, 682, 62, 11 11, 27, 297, 792, 72, 11 11, 31, 341, 143, 13, 11 |
11, 32, 352, 253, 23, 11 11, 33, 363, 363, 33, 11 11, 34, 374, 473, 43, 11 11, 35, 385, 583, 53, 11 11, 36, 396, 693, 63, 11 11, 41, 451, 154, 14, 11 11, 42, 462, 264, 24, 11 11, 43, 473, 374, 34, 11 11, 44, 484, 484, 44, 11 11, 45, 495, 594, 54, 11 12, 13, 156, 651, 31, 21 12, 14, 168, 861, 41, 21 12, 21, 252, 252, 12, 21 12, 22, 264, 462, 22, 21 12, 23, 276, 672, 32, 21 12, 24, 288, 882, 42, 21 12, 31, 372, 273, 13, 21 12, 32, 384, 483, 23, 21 |
12, 33, 396, 693, 33, 21 12, 41, 492, 294, 14, 21 13, 21, 273, 372, 12, 31 13, 22, 286, 682, 22, 31 13, 23, 299, 992, 32, 31 14, 21, 294, 492, 12, 41 21, 22, 462, 264, 22, 12 21, 23, 483, 384, 32, 12 21, 31, 651, 156, 13, 12 21, 32, 672, 276, 23, 12 21, 33, 693, 396, 33, 12 21, 41, 861, 168, 14, 12 21, 42, 882, 288, 24, 12 22, 31, 682, 286, 13, 22 31, 32, 992, 299, 23, 13 55, 99, 5445, 5445, 99, 55 77, 88, 6776, 6776, 88, 77 FIN |
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Trois chiffres de 100 à 999 101, 102, 10302, 20301, 201, 101 101, 103, 10403, 30401, 301, 101 101, 104, 10504, 40501, 401, 101 101, 105, 10605, 50601, 501, 101 101, 106, 10706, 60701, 601, 101 101, 107, 10807, 70801, 701, 101 101, 108, 10908, 80901, 801, 101 101, 111, 11211, 11211, 111, 101 101, 112, 11312, 21311, 211, 101 101, 113, 11413, 31411, 311, 101 101, 114, 11514, 41511, 411, 101 101, 115, 11615, 51611, 511, 101 101, 116, 11716, 61711, 611, 101 101, 117, 11817, 71811, 711, 101 101, 118, 11918, 81911, 811, 101 101, 121, 12221, 12221, 121, 101 101, 122, 12322, 22321, 221, 101 101, 123, 12423, 32421, 321, 101 101, 124, 12524, 42521, 421, 101 101, 125, 12625, 52621, 521, 101 101, 126, 12726, 62721, 621, 101 101, 127, 12827, 72821, 721, 101 101, 128, 12928, 82921, 821, 101 101, 131, 13231, 13231, 131, 101 101, 132, 13332, 23331, 231, 101 101, 133, 13433, 33431, 331, 101 101, 134, 13534, 43531, 431, 101 101, 135, 13635, 53631, 531, 101 101, 136, 13736, 63731, 631, 101 101, 137, 13837, 73831, 731, 101 101, 138, 13938, 83931, 831, 101 101, 141, 14241, 14241, 141, 101 101, 142, 14342, 24341, 241, 101 101, 143, 14443, 34441, 341, 101 101, 144, 14544, 44541, 441, 101 101, 145, 14645, 54641, 541, 101 101, 146, 14746, 64741, 641, 101 101, 147, 14847, 74841, 741, 101 101, 148, 14948, 84941, 841, 101 101, 151, 15251, 15251, 151, 101 101, 152, 15352, 25351, 251, 101 101, 153, 15453, 35451, 351, 101 101, 154, 15554, 45551, 451, 101 101, 155, 15655, 55651, 551, 101 101, 156, 15756, 65751, 651, 101 101, 157, 15857, 75851, 751, 101 101, 158, 15958, 85951, 851, 101 101, 161, 16261, 16261, 161, 101 101, 162, 16362, 26361, 261, 101 101, 163, 16463, 36461, 361, 101 101, 164, 16564, 46561, 461, 101 101, 165, 16665, 56661, 561, 101 101, 166, 16766, 66761, 661, 101 101, 167, 16867, 76861, 761, 101 101, 168, 16968, 86961, 861, 101 101, 171, 17271, 17271, 171, 101 101, 172, 17372, 27371, 271, 101 101, 173, 17473, 37471, 371, 101 101, 174, 17574, 47571, 471, 101 101, 175, 17675, 57671, 571, 101 101, 176, 17776, 67771, 671, 101 101, 177, 17877, 77871, 771, 101 101, 178, 17978, 87971, 871, 101 101, 181, 18281, 18281, 181, 101 101, 182, 18382, 28381, 281, 101 101, 183, 18483, 38481, 381, 101 101, 184, 18584, 48581, 481, 101 101, 185, 18685, 58681, 581, 101 101, 186, 18786, 68781, 681, 101 101, 187, 18887, 78881, 781, 101 101, 188, 18988, 88981, 881, 101 101, 191, 19291, 19291, 191, 101 101, 192, 19392, 29391, 291, 101 101, 193, 19493, 39491, 391, 101 101, 194, 19594, 49591, 491, 101 101, 195, 19695, 59691, 591, 101 101, 196, 19796, 69791, 691, 101 101, 197, 19897, 79891, 791, 101 101, 198, 19998, 89991, 891, 101 102, 103, 10506, 60501, 301, 201 102, 104, 10608, 80601, 401, 201 102, 111, 11322, 22311, 111, 201 102, 112, 11424, 42411, 211, 201 102, 113, 11526, 62511, 311, 201 102, 114, 11628, 82611, 411, 201 102, 121, 12342, 24321, 121, 201 102, 122, 12444, 44421, 221, 201 |
102, 123, 12546, 64521, 321, 201 102, 124, 12648, 84621, 421, 201 102, 131, 13362, 26331, 131, 201 102, 132, 13464, 46431, 231, 201 102, 133, 13566, 66531, 331, 201 102, 134, 13668, 86631, 431, 201 102, 141, 14382, 28341, 141, 201 102, 142, 14484, 48441, 241, 201 102, 143, 14586, 68541, 341, 201 102, 144, 14688, 88641, 441, 201 103, 111, 11433, 33411, 111, 301 103, 112, 11536, 63511, 211, 301 103, 113, 11639, 93611, 311, 301 103, 121, 12463, 36421, 121, 301 103, 122, 12566, 66521, 221, 301 103, 123, 12669, 96621, 321, 301 103, 131, 13493, 39431, 131, 301 103, 132, 13596, 69531, 231, 301 103, 133, 13699, 99631, 331, 301 104, 111, 11544, 44511, 111, 401 104, 112, 11648, 84611, 211, 401 104, 121, 12584, 48521, 121, 401 104, 122, 12688, 88621, 221, 401 105, 111, 11655, 55611, 111, 501 106, 111, 11766, 66711, 111, 601 107, 111, 11877, 77811, 111, 701 108, 111, 11988, 88911, 111, 801 111, 112, 12432, 23421, 211, 111 111, 113, 12543, 34521, 311, 111 111, 114, 12654, 45621, 411, 111 111, 115, 12765, 56721, 511, 111 111, 116, 12876, 67821, 611, 111 111, 117, 12987, 78921, 711, 111 111, 121, 13431, 13431, 121, 111 111, 122, 13542, 24531, 221, 111 111, 123, 13653, 35631, 321, 111 111, 124, 13764, 46731, 421, 111 111, 125, 13875, 57831, 521, 111 111, 126, 13986, 68931, 621, 111 111, 131, 14541, 14541, 131, 111 111, 132, 14652, 25641, 231, 111 111, 133, 14763, 36741, 331, 111 111, 134, 14874, 47841, 431, 111 111, 135, 14985, 58941, 531, 111 111, 141, 15651, 15651, 141, 111 111, 142, 15762, 26751, 241, 111 111, 143, 15873, 37851, 341, 111 111, 144, 15984, 48951, 441, 111 111, 151, 16761, 16761, 151, 111 111, 152, 16872, 27861, 251, 111 111, 153, 16983, 38961, 351, 111 111, 161, 17871, 17871, 161, 111 111, 162, 17982, 28971, 261, 111 111, 171, 18981, 18981, 171, 111 112, 113, 12656, 65621, 311, 211 112, 114, 12768, 86721, 411, 211 112, 121, 13552, 25531, 121, 211 112, 122, 13664, 46631, 221, 211 112, 123, 13776, 67731, 321, 211 112, 124, 13888, 88831, 421, 211 112, 131, 14672, 27641, 131, 211 112, 132, 14784, 48741, 231, 211 112, 133, 14896, 69841, 331, 211 112, 141, 15792, 29751, 141, 211 113, 121, 13673, 37631, 121, 311 113, 122, 13786, 68731, 221, 311 113, 123, 13899, 99831, 321, 311 114, 121, 13794, 49731, 121, 411 121, 122, 14762, 26741, 221, 121 121, 123, 14883, 38841, 321, 121 121, 131, 15851, 15851, 131, 121 121, 132, 15972, 27951, 231, 121 122, 131, 15982, 28951, 131, 221 … 301, 302, 90902, 20909, 203, 103 301, 311, 93611, 11639, 113, 103 301, 312, 93912, 21939, 213, 103 301, 321, 96621, 12669, 123, 103 301, 322, 96922, 22969, 223, 103 301, 331, 99631, 13699, 133, 103 301, 332, 99932, 23999, 233, 103 302, 311, 93922, 22939, 113, 203 302, 321, 96942, 24969, 123, 203 302, 331, 99962, 26999, 133, 203 311, 321, 99831, 13899, 123, 113 555, 979, 543345, 543345, 979, 555 707, 858, 606606, 606606, 858, 707 737, 888, 654456, 654456, 888, 737 777, 858, 666666, 666666, 858, 777 FIN |
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