332.205.300 和 0: 计算这两个数的所有公约数

数字 332.205.300 和 0 的所有公约数

求数字 332.205.300 和 0 的所有公约数等价于求其最大公约数的所有约数.

计算最大公约数, gcd:

零可被除自身以外的任何数字整除(零除以这些数字没有余数).

数字 332.205.300 的最大除数就是数字本身。


⇒ gcd (332.205.300; 0) = 332.205.300




要找到 'gcd' 的所有除数, 我们需要将其分解为质因数, 将其写为质数的乘积。

一个数的素数分解:找到相乘得到那个数的素数.


332.205.300 = 22 × 37 × 52 × 72 × 31
332.205.300 不是质数而是合数.



* 只能被 1 和自身整除的自然数称为素数. 素数正好有两个除数:1 和它自己.
* 合数是一个自然数,它至少有一个除 1 和它自身之外的除数.



乘以 'gcd' 的质因数:

将出现在最大公约数的素因数分解中的素因数相乘。 将它们以所有独特的组合相乘——产生不同结果的组合.


还要考虑素因数的指数 (例如: 32 = 3 × 3 = 9) .


还要将 1 添加到除数列表中。 所有数字都能被1整除.


下面列出了所有除数 - 按升序排列

除数名单:

既不是素数也不是合数 = 1
首要因素 = 2
首要因素 = 3
22 = 4
首要因素 = 5
2 × 3 = 6
首要因素 = 7
32 = 9
2 × 5 = 10
22 × 3 = 12
2 × 7 = 14
3 × 5 = 15
2 × 32 = 18
22 × 5 = 20
3 × 7 = 21
52 = 25
33 = 27
22 × 7 = 28
2 × 3 × 5 = 30
首要因素 = 31
5 × 7 = 35
22 × 32 = 36
2 × 3 × 7 = 42
32 × 5 = 45
72 = 49
2 × 52 = 50
2 × 33 = 54
22 × 3 × 5 = 60
2 × 31 = 62
32 × 7 = 63
2 × 5 × 7 = 70
3 × 52 = 75
34 = 81
22 × 3 × 7 = 84
2 × 32 × 5 = 90
3 × 31 = 93
2 × 72 = 98
22 × 52 = 100
3 × 5 × 7 = 105
22 × 33 = 108
22 × 31 = 124
2 × 32 × 7 = 126
33 × 5 = 135
22 × 5 × 7 = 140
3 × 72 = 147
2 × 3 × 52 = 150
5 × 31 = 155
2 × 34 = 162
52 × 7 = 175
22 × 32 × 5 = 180
2 × 3 × 31 = 186
33 × 7 = 189
22 × 72 = 196
2 × 3 × 5 × 7 = 210
7 × 31 = 217
32 × 52 = 225
35 = 243
5 × 72 = 245
22 × 32 × 7 = 252
2 × 33 × 5 = 270
32 × 31 = 279
2 × 3 × 72 = 294
22 × 3 × 52 = 300
2 × 5 × 31 = 310
32 × 5 × 7 = 315
22 × 34 = 324
2 × 52 × 7 = 350
22 × 3 × 31 = 372
2 × 33 × 7 = 378
34 × 5 = 405
22 × 3 × 5 × 7 = 420
2 × 7 × 31 = 434
32 × 72 = 441
2 × 32 × 52 = 450
3 × 5 × 31 = 465
2 × 35 = 486
2 × 5 × 72 = 490
3 × 52 × 7 = 525
22 × 33 × 5 = 540
2 × 32 × 31 = 558
34 × 7 = 567
22 × 3 × 72 = 588
22 × 5 × 31 = 620
2 × 32 × 5 × 7 = 630
3 × 7 × 31 = 651
33 × 52 = 675
22 × 52 × 7 = 700
36 = 729
3 × 5 × 72 = 735
22 × 33 × 7 = 756
52 × 31 = 775
2 × 34 × 5 = 810
33 × 31 = 837
22 × 7 × 31 = 868
2 × 32 × 72 = 882
22 × 32 × 52 = 900
2 × 3 × 5 × 31 = 930
33 × 5 × 7 = 945
22 × 35 = 972
22 × 5 × 72 = 980
2 × 3 × 52 × 7 = 1.050
5 × 7 × 31 = 1.085
22 × 32 × 31 = 1.116
2 × 34 × 7 = 1.134
35 × 5 = 1.215
52 × 72 = 1.225
22 × 32 × 5 × 7 = 1.260
2 × 3 × 7 × 31 = 1.302
33 × 72 = 1.323
2 × 33 × 52 = 1.350
32 × 5 × 31 = 1.395
2 × 36 = 1.458
2 × 3 × 5 × 72 = 1.470
72 × 31 = 1.519
2 × 52 × 31 = 1.550
32 × 52 × 7 = 1.575
22 × 34 × 5 = 1.620
2 × 33 × 31 = 1.674
35 × 7 = 1.701
22 × 32 × 72 = 1.764
22 × 3 × 5 × 31 = 1.860
2 × 33 × 5 × 7 = 1.890
32 × 7 × 31 = 1.953
34 × 52 = 2.025
22 × 3 × 52 × 7 = 2.100
2 × 5 × 7 × 31 = 2.170
37 = 2.187
32 × 5 × 72 = 2.205
22 × 34 × 7 = 2.268
3 × 52 × 31 = 2.325
2 × 35 × 5 = 2.430
2 × 52 × 72 = 2.450
34 × 31 = 2.511
22 × 3 × 7 × 31 = 2.604
2 × 33 × 72 = 2.646
22 × 33 × 52 = 2.700
2 × 32 × 5 × 31 = 2.790
34 × 5 × 7 = 2.835
22 × 36 = 2.916
22 × 3 × 5 × 72 = 2.940
2 × 72 × 31 = 3.038
22 × 52 × 31 = 3.100
2 × 32 × 52 × 7 = 3.150
3 × 5 × 7 × 31 = 3.255
22 × 33 × 31 = 3.348
2 × 35 × 7 = 3.402
36 × 5 = 3.645
3 × 52 × 72 = 3.675
22 × 33 × 5 × 7 = 3.780
2 × 32 × 7 × 31 = 3.906
34 × 72 = 3.969
2 × 34 × 52 = 4.050
33 × 5 × 31 = 4.185
22 × 5 × 7 × 31 = 4.340
2 × 37 = 4.374
2 × 32 × 5 × 72 = 4.410
3 × 72 × 31 = 4.557
2 × 3 × 52 × 31 = 4.650
33 × 52 × 7 = 4.725
22 × 35 × 5 = 4.860
22 × 52 × 72 = 4.900
2 × 34 × 31 = 5.022
36 × 7 = 5.103
22 × 33 × 72 = 5.292
52 × 7 × 31 = 5.425
22 × 32 × 5 × 31 = 5.580
2 × 34 × 5 × 7 = 5.670
33 × 7 × 31 = 5.859
35 × 52 = 6.075
22 × 72 × 31 = 6.076
22 × 32 × 52 × 7 = 6.300
2 × 3 × 5 × 7 × 31 = 6.510
33 × 5 × 72 = 6.615
22 × 35 × 7 = 6.804
32 × 52 × 31 = 6.975
2 × 36 × 5 = 7.290
2 × 3 × 52 × 72 = 7.350
35 × 31 = 7.533
5 × 72 × 31 = 7.595
22 × 32 × 7 × 31 = 7.812
2 × 34 × 72 = 7.938
22 × 34 × 52 = 8.100
2 × 33 × 5 × 31 = 8.370
35 × 5 × 7 = 8.505
22 × 37 = 8.748
22 × 32 × 5 × 72 = 8.820
2 × 3 × 72 × 31 = 9.114
22 × 3 × 52 × 31 = 9.300
2 × 33 × 52 × 7 = 9.450
32 × 5 × 7 × 31 = 9.765
22 × 34 × 31 = 10.044
2 × 36 × 7 = 10.206
2 × 52 × 7 × 31 = 10.850
37 × 5 = 10.935
32 × 52 × 72 = 11.025
22 × 34 × 5 × 7 = 11.340
2 × 33 × 7 × 31 = 11.718
35 × 72 = 11.907
2 × 35 × 52 = 12.150
34 × 5 × 31 = 12.555
22 × 3 × 5 × 7 × 31 = 13.020
2 × 33 × 5 × 72 = 13.230
32 × 72 × 31 = 13.671
2 × 32 × 52 × 31 = 13.950
34 × 52 × 7 = 14.175
22 × 36 × 5 = 14.580
22 × 3 × 52 × 72 = 14.700
2 × 35 × 31 = 15.066
2 × 5 × 72 × 31 = 15.190
37 × 7 = 15.309
22 × 34 × 72 = 15.876
3 × 52 × 7 × 31 = 16.275
22 × 33 × 5 × 31 = 16.740
2 × 35 × 5 × 7 = 17.010
34 × 7 × 31 = 17.577
36 × 52 = 18.225
此列表在下面继续...

... 此列表从上面继续
22 × 3 × 72 × 31 = 18.228
22 × 33 × 52 × 7 = 18.900
2 × 32 × 5 × 7 × 31 = 19.530
34 × 5 × 72 = 19.845
22 × 36 × 7 = 20.412
33 × 52 × 31 = 20.925
22 × 52 × 7 × 31 = 21.700
2 × 37 × 5 = 21.870
2 × 32 × 52 × 72 = 22.050
36 × 31 = 22.599
3 × 5 × 72 × 31 = 22.785
22 × 33 × 7 × 31 = 23.436
2 × 35 × 72 = 23.814
22 × 35 × 52 = 24.300
2 × 34 × 5 × 31 = 25.110
36 × 5 × 7 = 25.515
22 × 33 × 5 × 72 = 26.460
2 × 32 × 72 × 31 = 27.342
22 × 32 × 52 × 31 = 27.900
2 × 34 × 52 × 7 = 28.350
33 × 5 × 7 × 31 = 29.295
22 × 35 × 31 = 30.132
22 × 5 × 72 × 31 = 30.380
2 × 37 × 7 = 30.618
2 × 3 × 52 × 7 × 31 = 32.550
33 × 52 × 72 = 33.075
22 × 35 × 5 × 7 = 34.020
2 × 34 × 7 × 31 = 35.154
36 × 72 = 35.721
2 × 36 × 52 = 36.450
35 × 5 × 31 = 37.665
52 × 72 × 31 = 37.975
22 × 32 × 5 × 7 × 31 = 39.060
2 × 34 × 5 × 72 = 39.690
33 × 72 × 31 = 41.013
2 × 33 × 52 × 31 = 41.850
35 × 52 × 7 = 42.525
22 × 37 × 5 = 43.740
22 × 32 × 52 × 72 = 44.100
2 × 36 × 31 = 45.198
2 × 3 × 5 × 72 × 31 = 45.570
22 × 35 × 72 = 47.628
32 × 52 × 7 × 31 = 48.825
22 × 34 × 5 × 31 = 50.220
2 × 36 × 5 × 7 = 51.030
35 × 7 × 31 = 52.731
37 × 52 = 54.675
22 × 32 × 72 × 31 = 54.684
22 × 34 × 52 × 7 = 56.700
2 × 33 × 5 × 7 × 31 = 58.590
35 × 5 × 72 = 59.535
22 × 37 × 7 = 61.236
34 × 52 × 31 = 62.775
22 × 3 × 52 × 7 × 31 = 65.100
2 × 33 × 52 × 72 = 66.150
37 × 31 = 67.797
32 × 5 × 72 × 31 = 68.355
22 × 34 × 7 × 31 = 70.308
2 × 36 × 72 = 71.442
22 × 36 × 52 = 72.900
2 × 35 × 5 × 31 = 75.330
2 × 52 × 72 × 31 = 75.950
37 × 5 × 7 = 76.545
22 × 34 × 5 × 72 = 79.380
2 × 33 × 72 × 31 = 82.026
22 × 33 × 52 × 31 = 83.700
2 × 35 × 52 × 7 = 85.050
34 × 5 × 7 × 31 = 87.885
22 × 36 × 31 = 90.396
22 × 3 × 5 × 72 × 31 = 91.140
2 × 32 × 52 × 7 × 31 = 97.650
34 × 52 × 72 = 99.225
22 × 36 × 5 × 7 = 102.060
2 × 35 × 7 × 31 = 105.462
37 × 72 = 107.163
2 × 37 × 52 = 109.350
36 × 5 × 31 = 112.995
3 × 52 × 72 × 31 = 113.925
22 × 33 × 5 × 7 × 31 = 117.180
2 × 35 × 5 × 72 = 119.070
34 × 72 × 31 = 123.039
2 × 34 × 52 × 31 = 125.550
36 × 52 × 7 = 127.575
22 × 33 × 52 × 72 = 132.300
2 × 37 × 31 = 135.594
2 × 32 × 5 × 72 × 31 = 136.710
22 × 36 × 72 = 142.884
33 × 52 × 7 × 31 = 146.475
22 × 35 × 5 × 31 = 150.660
22 × 52 × 72 × 31 = 151.900
2 × 37 × 5 × 7 = 153.090
36 × 7 × 31 = 158.193
22 × 33 × 72 × 31 = 164.052
22 × 35 × 52 × 7 = 170.100
2 × 34 × 5 × 7 × 31 = 175.770
36 × 5 × 72 = 178.605
35 × 52 × 31 = 188.325
22 × 32 × 52 × 7 × 31 = 195.300
2 × 34 × 52 × 72 = 198.450
33 × 5 × 72 × 31 = 205.065
22 × 35 × 7 × 31 = 210.924
2 × 37 × 72 = 214.326
22 × 37 × 52 = 218.700
2 × 36 × 5 × 31 = 225.990
2 × 3 × 52 × 72 × 31 = 227.850
22 × 35 × 5 × 72 = 238.140
2 × 34 × 72 × 31 = 246.078
22 × 34 × 52 × 31 = 251.100
2 × 36 × 52 × 7 = 255.150
35 × 5 × 7 × 31 = 263.655
22 × 37 × 31 = 271.188
22 × 32 × 5 × 72 × 31 = 273.420
2 × 33 × 52 × 7 × 31 = 292.950
35 × 52 × 72 = 297.675
22 × 37 × 5 × 7 = 306.180
2 × 36 × 7 × 31 = 316.386
37 × 5 × 31 = 338.985
32 × 52 × 72 × 31 = 341.775
22 × 34 × 5 × 7 × 31 = 351.540
2 × 36 × 5 × 72 = 357.210
35 × 72 × 31 = 369.117
2 × 35 × 52 × 31 = 376.650
37 × 52 × 7 = 382.725
22 × 34 × 52 × 72 = 396.900
2 × 33 × 5 × 72 × 31 = 410.130
22 × 37 × 72 = 428.652
34 × 52 × 7 × 31 = 439.425
22 × 36 × 5 × 31 = 451.980
22 × 3 × 52 × 72 × 31 = 455.700
37 × 7 × 31 = 474.579
22 × 34 × 72 × 31 = 492.156
22 × 36 × 52 × 7 = 510.300
2 × 35 × 5 × 7 × 31 = 527.310
37 × 5 × 72 = 535.815
36 × 52 × 31 = 564.975
22 × 33 × 52 × 7 × 31 = 585.900
2 × 35 × 52 × 72 = 595.350
34 × 5 × 72 × 31 = 615.195
22 × 36 × 7 × 31 = 632.772
2 × 37 × 5 × 31 = 677.970
2 × 32 × 52 × 72 × 31 = 683.550
22 × 36 × 5 × 72 = 714.420
2 × 35 × 72 × 31 = 738.234
22 × 35 × 52 × 31 = 753.300
2 × 37 × 52 × 7 = 765.450
36 × 5 × 7 × 31 = 790.965
22 × 33 × 5 × 72 × 31 = 820.260
2 × 34 × 52 × 7 × 31 = 878.850
36 × 52 × 72 = 893.025
2 × 37 × 7 × 31 = 949.158
33 × 52 × 72 × 31 = 1.025.325
22 × 35 × 5 × 7 × 31 = 1.054.620
2 × 37 × 5 × 72 = 1.071.630
36 × 72 × 31 = 1.107.351
2 × 36 × 52 × 31 = 1.129.950
22 × 35 × 52 × 72 = 1.190.700
2 × 34 × 5 × 72 × 31 = 1.230.390
35 × 52 × 7 × 31 = 1.318.275
22 × 37 × 5 × 31 = 1.355.940
22 × 32 × 52 × 72 × 31 = 1.367.100
22 × 35 × 72 × 31 = 1.476.468
22 × 37 × 52 × 7 = 1.530.900
2 × 36 × 5 × 7 × 31 = 1.581.930
37 × 52 × 31 = 1.694.925
22 × 34 × 52 × 7 × 31 = 1.757.700
2 × 36 × 52 × 72 = 1.786.050
35 × 5 × 72 × 31 = 1.845.585
22 × 37 × 7 × 31 = 1.898.316
2 × 33 × 52 × 72 × 31 = 2.050.650
22 × 37 × 5 × 72 = 2.143.260
2 × 36 × 72 × 31 = 2.214.702
22 × 36 × 52 × 31 = 2.259.900
37 × 5 × 7 × 31 = 2.372.895
22 × 34 × 5 × 72 × 31 = 2.460.780
2 × 35 × 52 × 7 × 31 = 2.636.550
37 × 52 × 72 = 2.679.075
34 × 52 × 72 × 31 = 3.075.975
22 × 36 × 5 × 7 × 31 = 3.163.860
37 × 72 × 31 = 3.322.053
2 × 37 × 52 × 31 = 3.389.850
22 × 36 × 52 × 72 = 3.572.100
2 × 35 × 5 × 72 × 31 = 3.691.170
36 × 52 × 7 × 31 = 3.954.825
22 × 33 × 52 × 72 × 31 = 4.101.300
22 × 36 × 72 × 31 = 4.429.404
2 × 37 × 5 × 7 × 31 = 4.745.790
22 × 35 × 52 × 7 × 31 = 5.273.100
2 × 37 × 52 × 72 = 5.358.150
36 × 5 × 72 × 31 = 5.536.755
2 × 34 × 52 × 72 × 31 = 6.151.950
2 × 37 × 72 × 31 = 6.644.106
22 × 37 × 52 × 31 = 6.779.700
22 × 35 × 5 × 72 × 31 = 7.382.340
2 × 36 × 52 × 7 × 31 = 7.909.650
35 × 52 × 72 × 31 = 9.227.925
22 × 37 × 5 × 7 × 31 = 9.491.580
22 × 37 × 52 × 72 = 10.716.300
2 × 36 × 5 × 72 × 31 = 11.073.510
37 × 52 × 7 × 31 = 11.864.475
22 × 34 × 52 × 72 × 31 = 12.303.900
22 × 37 × 72 × 31 = 13.288.212
22 × 36 × 52 × 7 × 31 = 15.819.300
37 × 5 × 72 × 31 = 16.610.265
2 × 35 × 52 × 72 × 31 = 18.455.850
22 × 36 × 5 × 72 × 31 = 22.147.020
2 × 37 × 52 × 7 × 31 = 23.728.950
36 × 52 × 72 × 31 = 27.683.775
2 × 37 × 5 × 72 × 31 = 33.220.530
22 × 35 × 52 × 72 × 31 = 36.911.700
22 × 37 × 52 × 7 × 31 = 47.457.900
2 × 36 × 52 × 72 × 31 = 55.367.550
22 × 37 × 5 × 72 × 31 = 66.441.060
37 × 52 × 72 × 31 = 83.051.325
22 × 36 × 52 × 72 × 31 = 110.735.100
2 × 37 × 52 × 72 × 31 = 166.102.650
22 × 37 × 52 × 72 × 31 = 332.205.300

332.205.3000 有 432 个公约数:
1; 2; 3; 4; 5; 6; 7; 9; 10; 12; 14; 15; 18; 20; 21; 25; 27; 28; 30; 31; 35; 36; 42; 45; 49; 50; 54; 60; 62; 63; 70; 75; 81; 84; 90; 93; 98; 100; 105; 108; 124; 126; 135; 140; 147; 150; 155; 162; 175; 180; 186; 189; 196; 210; 217; 225; 243; 245; 252; 270; 279; 294; 300; 310; 315; 324; 350; 372; 378; 405; 420; 434; 441; 450; 465; 486; 490; 525; 540; 558; 567; 588; 620; 630; 651; 675; 700; 729; 735; 756; 775; 810; 837; 868; 882; 900; 930; 945; 972; 980; 1.050; 1.085; 1.116; 1.134; 1.215; 1.225; 1.260; 1.302; 1.323; 1.350; 1.395; 1.458; 1.470; 1.519; 1.550; 1.575; 1.620; 1.674; 1.701; 1.764; 1.860; 1.890; 1.953; 2.025; 2.100; 2.170; 2.187; 2.205; 2.268; 2.325; 2.430; 2.450; 2.511; 2.604; 2.646; 2.700; 2.790; 2.835; 2.916; 2.940; 3.038; 3.100; 3.150; 3.255; 3.348; 3.402; 3.645; 3.675; 3.780; 3.906; 3.969; 4.050; 4.185; 4.340; 4.374; 4.410; 4.557; 4.650; 4.725; 4.860; 4.900; 5.022; 5.103; 5.292; 5.425; 5.580; 5.670; 5.859; 6.075; 6.076; 6.300; 6.510; 6.615; 6.804; 6.975; 7.290; 7.350; 7.533; 7.595; 7.812; 7.938; 8.100; 8.370; 8.505; 8.748; 8.820; 9.114; 9.300; 9.450; 9.765; 10.044; 10.206; 10.850; 10.935; 11.025; 11.340; 11.718; 11.907; 12.150; 12.555; 13.020; 13.230; 13.671; 13.950; 14.175; 14.580; 14.700; 15.066; 15.190; 15.309; 15.876; 16.275; 16.740; 17.010; 17.577; 18.225; 18.228; 18.900; 19.530; 19.845; 20.412; 20.925; 21.700; 21.870; 22.050; 22.599; 22.785; 23.436; 23.814; 24.300; 25.110; 25.515; 26.460; 27.342; 27.900; 28.350; 29.295; 30.132; 30.380; 30.618; 32.550; 33.075; 34.020; 35.154; 35.721; 36.450; 37.665; 37.975; 39.060; 39.690; 41.013; 41.850; 42.525; 43.740; 44.100; 45.198; 45.570; 47.628; 48.825; 50.220; 51.030; 52.731; 54.675; 54.684; 56.700; 58.590; 59.535; 61.236; 62.775; 65.100; 66.150; 67.797; 68.355; 70.308; 71.442; 72.900; 75.330; 75.950; 76.545; 79.380; 82.026; 83.700; 85.050; 87.885; 90.396; 91.140; 97.650; 99.225; 102.060; 105.462; 107.163; 109.350; 112.995; 113.925; 117.180; 119.070; 123.039; 125.550; 127.575; 132.300; 135.594; 136.710; 142.884; 146.475; 150.660; 151.900; 153.090; 158.193; 164.052; 170.100; 175.770; 178.605; 188.325; 195.300; 198.450; 205.065; 210.924; 214.326; 218.700; 225.990; 227.850; 238.140; 246.078; 251.100; 255.150; 263.655; 271.188; 273.420; 292.950; 297.675; 306.180; 316.386; 338.985; 341.775; 351.540; 357.210; 369.117; 376.650; 382.725; 396.900; 410.130; 428.652; 439.425; 451.980; 455.700; 474.579; 492.156; 510.300; 527.310; 535.815; 564.975; 585.900; 595.350; 615.195; 632.772; 677.970; 683.550; 714.420; 738.234; 753.300; 765.450; 790.965; 820.260; 878.850; 893.025; 949.158; 1.025.325; 1.054.620; 1.071.630; 1.107.351; 1.129.950; 1.190.700; 1.230.390; 1.318.275; 1.355.940; 1.367.100; 1.476.468; 1.530.900; 1.581.930; 1.694.925; 1.757.700; 1.786.050; 1.845.585; 1.898.316; 2.050.650; 2.143.260; 2.214.702; 2.259.900; 2.372.895; 2.460.780; 2.636.550; 2.679.075; 3.075.975; 3.163.860; 3.322.053; 3.389.850; 3.572.100; 3.691.170; 3.954.825; 4.101.300; 4.429.404; 4.745.790; 5.273.100; 5.358.150; 5.536.755; 6.151.950; 6.644.106; 6.779.700; 7.382.340; 7.909.650; 9.227.925; 9.491.580; 10.716.300; 11.073.510; 11.864.475; 12.303.900; 13.288.212; 15.819.300; 16.610.265; 18.455.850; 22.147.020; 23.728.950; 27.683.775; 33.220.530; 36.911.700; 47.457.900; 55.367.550; 66.441.060; 83.051.325; 110.735.100; 166.102.650332.205.300
其中有 5 个素数: 2; 3; 5; 7 和 31

计算一个或两个给定数字的所有除数

如何计算(如何求)一个数的所有除数:

如果该数是合数,则将其分解为素因数(数的素因数分解)。 然后将它们所有独特组合中的主要因子相乘,得到不同的结果。

如何计算两个数的所有公约数:

两个数的所有公约数都是最大公约数的所有约数。

计算这两个数字的最大公约数。

然后将最大公约数分解为质因数。 最后,将产生不同结果的所有质因数相乘,以它们所有独特的组合。

一个或两个数字的所有最新计算除数

除数,公约数,最大公约数,gcd(或也称为最高公约数,hcf)。

  • 如果数字“t”是数字“a”的除数,那么在“t”的素因式分解中,我们将只遇到也出现在“a”的素因式分解中的素因数。
  • 如果涉及指数,则在“t”的素因数分解中找到的任何基数的最大值最多等于“a”的素数因数分解中涉及的同一基数的指数。
  • 笔记: 23 = 2 × 2 × 2 = 8. 我们说 2 的 3 次方。 在此示例中,3 是指数,2 是底数。 指数表示底数与自身相乘的次数。 23 是幂,8 是幂的值。
  • 例如,12 是 120 的除数 - 将 120 除以 12 时余数为零。
  • 让我们看一下这两个数的素因数分解,并注意在这两个数的素数分解中出现的所有基数和指数:
  • 12 = 2 × 2 × 3 = 22 × 3
  • 120 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5
  • 120 包含了 12 的所有质因数,并且它的所有底的指数都高于 12 的指数。
  • 如果“t”是“a”和“b”的公约数,则“t”的素数分解只包含“a”和“b”的素数分解中涉及的公共素因数。
  • 如果涉及指数,则在“t”的素因数分解中找到的任何基的指数的最大值至多等于“a”的素因数分解中涉及的同一基的指数的最小值 ”和“b”。
  • 例如,12 是 48 和 360 的公约数。
  • 将 48 或 360 除以 12 时余数为零。
  • 这里有三个数字 12、48 和 360 的所有素数分解:
  • 12 = 22 × 3
  • 48 = 24 × 3
  • 360 = 23 × 32 × 5
  • 请注意,48 和 360 有更多的除数: 2, 3, 4, 6, 8, 12, 24. 在这些数字中,24 是 48 和 360 的最大公约数,gcd(或最大公约数,hcf)。
  • 两个数“a”和“b”的最大公约数 gcd 是“a”和“b”的素数分解中涉及的所有公素因数的乘积,每个素数都取最低指数。
  • 根据此规则,可以计算出几个数的最大公约数,如下例所示。
  • gcd (1260; 3024; 5544) = ?
  • 1260 = 22 × 32
  • 3024 = 24 × 32 × 7
  • 5544 = 23 × 32 × 7 × 11
  • 这三个数的共同质因数是:
  • 2 - 它的最低指数是 (2; 3; 4) = 2 的最小值
  • 3 - 它的最低指数是 (2; 2; 2) 中的最小值 = 2
  • gcd (1260; 3024; 5544) = 22 × 32 = 252
  • 互质数:
  • 如果两个数“a”和“b”除了 1 之外没有其他公约数,则 gcd (a, b) = 1,并且数“a”和“b”称为互质数。
  • 两个数的最大公约数的所有除数:
  • 如果“a”和“b”不是互质的,那么“a”和“b”的每个公约数都是“a”和“b”的最大公约数的约数。