17.635.800: 计算该数的所有除数和素因数

数字 17.635.800 的所有除数 17.635.800

1. 将数字 17.635.800 分解为质因数：

一个数的素数分解： 找到相乘得到那个数的素数.

17.635.800 = 23 × 3 × 52 × 7 × 13 × 17 × 19
17.635.800 不是质数而是合数.

» 在线计算器. 数是素数还是合数？ 合数的素数分解

* 只能被 1 和自身整除的自然数称为素数. 一个素数正好有两个除数： 1 和这个数本身.
* 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.


2. 乘以数字 17.635.800 的质因数

乘以这个数的素因数分解所涉及的素因数。 制作他们所有的独特组合——那些产生不同结果的组合.

还要考虑这些素数的指数.

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
23 = 8
2 × 5 = 10
22 × 3 = 12
首要因素 = 13
2 × 7 = 14
3 × 5 = 15
首要因素 = 17
首要因素 = 19
22 × 5 = 20
3 × 7 = 21
23 × 3 = 24
52 = 25
2 × 13 = 26
22 × 7 = 28
2 × 3 × 5 = 30
2 × 17 = 34
5 × 7 = 35
2 × 19 = 38
3 × 13 = 39
23 × 5 = 40
2 × 3 × 7 = 42
2 × 52 = 50
3 × 17 = 51
22 × 13 = 52
23 × 7 = 56
3 × 19 = 57
22 × 3 × 5 = 60
5 × 13 = 65
22 × 17 = 68
2 × 5 × 7 = 70
3 × 52 = 75
22 × 19 = 76
2 × 3 × 13 = 78
22 × 3 × 7 = 84
5 × 17 = 85
7 × 13 = 91
5 × 19 = 95
22 × 52 = 100
2 × 3 × 17 = 102
23 × 13 = 104
3 × 5 × 7 = 105
2 × 3 × 19 = 114
7 × 17 = 119
23 × 3 × 5 = 120
2 × 5 × 13 = 130
7 × 19 = 133
23 × 17 = 136
22 × 5 × 7 = 140
2 × 3 × 52 = 150
23 × 19 = 152
22 × 3 × 13 = 156
23 × 3 × 7 = 168
2 × 5 × 17 = 170
52 × 7 = 175
2 × 7 × 13 = 182
2 × 5 × 19 = 190
3 × 5 × 13 = 195
23 × 52 = 200
22 × 3 × 17 = 204
2 × 3 × 5 × 7 = 210
13 × 17 = 221
22 × 3 × 19 = 228
2 × 7 × 17 = 238
13 × 19 = 247
3 × 5 × 17 = 255
22 × 5 × 13 = 260
2 × 7 × 19 = 266
3 × 7 × 13 = 273
23 × 5 × 7 = 280
3 × 5 × 19 = 285
22 × 3 × 52 = 300
23 × 3 × 13 = 312
17 × 19 = 323
52 × 13 = 325
22 × 5 × 17 = 340
2 × 52 × 7 = 350
3 × 7 × 17 = 357
22 × 7 × 13 = 364
22 × 5 × 19 = 380
2 × 3 × 5 × 13 = 390
3 × 7 × 19 = 399
23 × 3 × 17 = 408
22 × 3 × 5 × 7 = 420
52 × 17 = 425
2 × 13 × 17 = 442
5 × 7 × 13 = 455
23 × 3 × 19 = 456
52 × 19 = 475
22 × 7 × 17 = 476
2 × 13 × 19 = 494
2 × 3 × 5 × 17 = 510
23 × 5 × 13 = 520
3 × 52 × 7 = 525
22 × 7 × 19 = 532
2 × 3 × 7 × 13 = 546
2 × 3 × 5 × 19 = 570
5 × 7 × 17 = 595
23 × 3 × 52 = 600
2 × 17 × 19 = 646
2 × 52 × 13 = 650
3 × 13 × 17 = 663
5 × 7 × 19 = 665
23 × 5 × 17 = 680
22 × 52 × 7 = 700
2 × 3 × 7 × 17 = 714
23 × 7 × 13 = 728
3 × 13 × 19 = 741
23 × 5 × 19 = 760
22 × 3 × 5 × 13 = 780
2 × 3 × 7 × 19 = 798
23 × 3 × 5 × 7 = 840
2 × 52 × 17 = 850
22 × 13 × 17 = 884
2 × 5 × 7 × 13 = 910
2 × 52 × 19 = 950
23 × 7 × 17 = 952
3 × 17 × 19 = 969
3 × 52 × 13 = 975
22 × 13 × 19 = 988
22 × 3 × 5 × 17 = 1.020
2 × 3 × 52 × 7 = 1.050
23 × 7 × 19 = 1.064
22 × 3 × 7 × 13 = 1.092
5 × 13 × 17 = 1.105
22 × 3 × 5 × 19 = 1.140
2 × 5 × 7 × 17 = 1.190
5 × 13 × 19 = 1.235
3 × 52 × 17 = 1.275
22 × 17 × 19 = 1.292
22 × 52 × 13 = 1.300
2 × 3 × 13 × 17 = 1.326
2 × 5 × 7 × 19 = 1.330
3 × 5 × 7 × 13 = 1.365
23 × 52 × 7 = 1.400
3 × 52 × 19 = 1.425
22 × 3 × 7 × 17 = 1.428
2 × 3 × 13 × 19 = 1.482
7 × 13 × 17 = 1.547
23 × 3 × 5 × 13 = 1.560
22 × 3 × 7 × 19 = 1.596
5 × 17 × 19 = 1.615
22 × 52 × 17 = 1.700
7 × 13 × 19 = 1.729
23 × 13 × 17 = 1.768
3 × 5 × 7 × 17 = 1.785
22 × 5 × 7 × 13 = 1.820
22 × 52 × 19 = 1.900
2 × 3 × 17 × 19 = 1.938
2 × 3 × 52 × 13 = 1.950
23 × 13 × 19 = 1.976
3 × 5 × 7 × 19 = 1.995
23 × 3 × 5 × 17 = 2.040
22 × 3 × 52 × 7 = 2.100
23 × 3 × 7 × 13 = 2.184
2 × 5 × 13 × 17 = 2.210
7 × 17 × 19 = 2.261
52 × 7 × 13 = 2.275
23 × 3 × 5 × 19 = 2.280
22 × 5 × 7 × 17 = 2.380
2 × 5 × 13 × 19 = 2.470
2 × 3 × 52 × 17 = 2.550
23 × 17 × 19 = 2.584
23 × 52 × 13 = 2.600
22 × 3 × 13 × 17 = 2.652
22 × 5 × 7 × 19 = 2.660
2 × 3 × 5 × 7 × 13 = 2.730
2 × 3 × 52 × 19 = 2.850
23 × 3 × 7 × 17 = 2.856
22 × 3 × 13 × 19 = 2.964
52 × 7 × 17 = 2.975
2 × 7 × 13 × 17 = 3.094
23 × 3 × 7 × 19 = 3.192
2 × 5 × 17 × 19 = 3.230
3 × 5 × 13 × 17 = 3.315
52 × 7 × 19 = 3.325
23 × 52 × 17 = 3.400
2 × 7 × 13 × 19 = 3.458
2 × 3 × 5 × 7 × 17 = 3.570
23 × 5 × 7 × 13 = 3.640
3 × 5 × 13 × 19 = 3.705
23 × 52 × 19 = 3.800
22 × 3 × 17 × 19 = 3.876
22 × 3 × 52 × 13 = 3.900
2 × 3 × 5 × 7 × 19 = 3.990
13 × 17 × 19 = 4.199
此列表在下面继续...

... 此列表从上面继续
23 × 3 × 52 × 7 = 4.200
22 × 5 × 13 × 17 = 4.420
2 × 7 × 17 × 19 = 4.522
2 × 52 × 7 × 13 = 4.550
3 × 7 × 13 × 17 = 4.641
23 × 5 × 7 × 17 = 4.760
3 × 5 × 17 × 19 = 4.845
22 × 5 × 13 × 19 = 4.940
22 × 3 × 52 × 17 = 5.100
3 × 7 × 13 × 19 = 5.187
23 × 3 × 13 × 17 = 5.304
23 × 5 × 7 × 19 = 5.320
22 × 3 × 5 × 7 × 13 = 5.460
52 × 13 × 17 = 5.525
22 × 3 × 52 × 19 = 5.700
23 × 3 × 13 × 19 = 5.928
2 × 52 × 7 × 17 = 5.950
52 × 13 × 19 = 6.175
22 × 7 × 13 × 17 = 6.188
22 × 5 × 17 × 19 = 6.460
2 × 3 × 5 × 13 × 17 = 6.630
2 × 52 × 7 × 19 = 6.650
3 × 7 × 17 × 19 = 6.783
3 × 52 × 7 × 13 = 6.825
22 × 7 × 13 × 19 = 6.916
22 × 3 × 5 × 7 × 17 = 7.140
2 × 3 × 5 × 13 × 19 = 7.410
5 × 7 × 13 × 17 = 7.735
23 × 3 × 17 × 19 = 7.752
23 × 3 × 52 × 13 = 7.800
22 × 3 × 5 × 7 × 19 = 7.980
52 × 17 × 19 = 8.075
2 × 13 × 17 × 19 = 8.398
5 × 7 × 13 × 19 = 8.645
23 × 5 × 13 × 17 = 8.840
3 × 52 × 7 × 17 = 8.925
22 × 7 × 17 × 19 = 9.044
22 × 52 × 7 × 13 = 9.100
2 × 3 × 7 × 13 × 17 = 9.282
2 × 3 × 5 × 17 × 19 = 9.690
23 × 5 × 13 × 19 = 9.880
3 × 52 × 7 × 19 = 9.975
23 × 3 × 52 × 17 = 10.200
2 × 3 × 7 × 13 × 19 = 10.374
23 × 3 × 5 × 7 × 13 = 10.920
2 × 52 × 13 × 17 = 11.050
5 × 7 × 17 × 19 = 11.305
23 × 3 × 52 × 19 = 11.400
22 × 52 × 7 × 17 = 11.900
2 × 52 × 13 × 19 = 12.350
23 × 7 × 13 × 17 = 12.376
3 × 13 × 17 × 19 = 12.597
23 × 5 × 17 × 19 = 12.920
22 × 3 × 5 × 13 × 17 = 13.260
22 × 52 × 7 × 19 = 13.300
2 × 3 × 7 × 17 × 19 = 13.566
2 × 3 × 52 × 7 × 13 = 13.650
23 × 7 × 13 × 19 = 13.832
23 × 3 × 5 × 7 × 17 = 14.280
22 × 3 × 5 × 13 × 19 = 14.820
2 × 5 × 7 × 13 × 17 = 15.470
23 × 3 × 5 × 7 × 19 = 15.960
2 × 52 × 17 × 19 = 16.150
3 × 52 × 13 × 17 = 16.575
22 × 13 × 17 × 19 = 16.796
2 × 5 × 7 × 13 × 19 = 17.290
2 × 3 × 52 × 7 × 17 = 17.850
23 × 7 × 17 × 19 = 18.088
23 × 52 × 7 × 13 = 18.200
3 × 52 × 13 × 19 = 18.525
22 × 3 × 7 × 13 × 17 = 18.564
22 × 3 × 5 × 17 × 19 = 19.380
2 × 3 × 52 × 7 × 19 = 19.950
22 × 3 × 7 × 13 × 19 = 20.748
5 × 13 × 17 × 19 = 20.995
22 × 52 × 13 × 17 = 22.100
2 × 5 × 7 × 17 × 19 = 22.610
3 × 5 × 7 × 13 × 17 = 23.205
23 × 52 × 7 × 17 = 23.800
3 × 52 × 17 × 19 = 24.225
22 × 52 × 13 × 19 = 24.700
2 × 3 × 13 × 17 × 19 = 25.194
3 × 5 × 7 × 13 × 19 = 25.935
23 × 3 × 5 × 13 × 17 = 26.520
23 × 52 × 7 × 19 = 26.600
22 × 3 × 7 × 17 × 19 = 27.132
22 × 3 × 52 × 7 × 13 = 27.300
7 × 13 × 17 × 19 = 29.393
23 × 3 × 5 × 13 × 19 = 29.640
22 × 5 × 7 × 13 × 17 = 30.940
22 × 52 × 17 × 19 = 32.300
2 × 3 × 52 × 13 × 17 = 33.150
23 × 13 × 17 × 19 = 33.592
3 × 5 × 7 × 17 × 19 = 33.915
22 × 5 × 7 × 13 × 19 = 34.580
22 × 3 × 52 × 7 × 17 = 35.700
2 × 3 × 52 × 13 × 19 = 37.050
23 × 3 × 7 × 13 × 17 = 37.128
52 × 7 × 13 × 17 = 38.675
23 × 3 × 5 × 17 × 19 = 38.760
22 × 3 × 52 × 7 × 19 = 39.900
23 × 3 × 7 × 13 × 19 = 41.496
2 × 5 × 13 × 17 × 19 = 41.990
52 × 7 × 13 × 19 = 43.225
23 × 52 × 13 × 17 = 44.200
22 × 5 × 7 × 17 × 19 = 45.220
2 × 3 × 5 × 7 × 13 × 17 = 46.410
2 × 3 × 52 × 17 × 19 = 48.450
23 × 52 × 13 × 19 = 49.400
22 × 3 × 13 × 17 × 19 = 50.388
2 × 3 × 5 × 7 × 13 × 19 = 51.870
23 × 3 × 7 × 17 × 19 = 54.264
23 × 3 × 52 × 7 × 13 = 54.600
52 × 7 × 17 × 19 = 56.525
2 × 7 × 13 × 17 × 19 = 58.786
23 × 5 × 7 × 13 × 17 = 61.880
3 × 5 × 13 × 17 × 19 = 62.985
23 × 52 × 17 × 19 = 64.600
22 × 3 × 52 × 13 × 17 = 66.300
2 × 3 × 5 × 7 × 17 × 19 = 67.830
23 × 5 × 7 × 13 × 19 = 69.160
23 × 3 × 52 × 7 × 17 = 71.400
22 × 3 × 52 × 13 × 19 = 74.100
2 × 52 × 7 × 13 × 17 = 77.350
23 × 3 × 52 × 7 × 19 = 79.800
22 × 5 × 13 × 17 × 19 = 83.980
2 × 52 × 7 × 13 × 19 = 86.450
3 × 7 × 13 × 17 × 19 = 88.179
23 × 5 × 7 × 17 × 19 = 90.440
22 × 3 × 5 × 7 × 13 × 17 = 92.820
22 × 3 × 52 × 17 × 19 = 96.900
23 × 3 × 13 × 17 × 19 = 100.776
22 × 3 × 5 × 7 × 13 × 19 = 103.740
52 × 13 × 17 × 19 = 104.975
2 × 52 × 7 × 17 × 19 = 113.050
3 × 52 × 7 × 13 × 17 = 116.025
22 × 7 × 13 × 17 × 19 = 117.572
2 × 3 × 5 × 13 × 17 × 19 = 125.970
3 × 52 × 7 × 13 × 19 = 129.675
23 × 3 × 52 × 13 × 17 = 132.600
22 × 3 × 5 × 7 × 17 × 19 = 135.660
5 × 7 × 13 × 17 × 19 = 146.965
23 × 3 × 52 × 13 × 19 = 148.200
22 × 52 × 7 × 13 × 17 = 154.700
23 × 5 × 13 × 17 × 19 = 167.960
3 × 52 × 7 × 17 × 19 = 169.575
22 × 52 × 7 × 13 × 19 = 172.900
2 × 3 × 7 × 13 × 17 × 19 = 176.358
23 × 3 × 5 × 7 × 13 × 17 = 185.640
23 × 3 × 52 × 17 × 19 = 193.800
23 × 3 × 5 × 7 × 13 × 19 = 207.480
2 × 52 × 13 × 17 × 19 = 209.950
22 × 52 × 7 × 17 × 19 = 226.100
2 × 3 × 52 × 7 × 13 × 17 = 232.050
23 × 7 × 13 × 17 × 19 = 235.144
22 × 3 × 5 × 13 × 17 × 19 = 251.940
2 × 3 × 52 × 7 × 13 × 19 = 259.350
23 × 3 × 5 × 7 × 17 × 19 = 271.320
2 × 5 × 7 × 13 × 17 × 19 = 293.930
23 × 52 × 7 × 13 × 17 = 309.400
3 × 52 × 13 × 17 × 19 = 314.925
2 × 3 × 52 × 7 × 17 × 19 = 339.150
23 × 52 × 7 × 13 × 19 = 345.800
22 × 3 × 7 × 13 × 17 × 19 = 352.716
22 × 52 × 13 × 17 × 19 = 419.900
3 × 5 × 7 × 13 × 17 × 19 = 440.895
23 × 52 × 7 × 17 × 19 = 452.200
22 × 3 × 52 × 7 × 13 × 17 = 464.100
23 × 3 × 5 × 13 × 17 × 19 = 503.880
22 × 3 × 52 × 7 × 13 × 19 = 518.700
22 × 5 × 7 × 13 × 17 × 19 = 587.860
2 × 3 × 52 × 13 × 17 × 19 = 629.850
22 × 3 × 52 × 7 × 17 × 19 = 678.300
23 × 3 × 7 × 13 × 17 × 19 = 705.432
52 × 7 × 13 × 17 × 19 = 734.825
23 × 52 × 13 × 17 × 19 = 839.800
2 × 3 × 5 × 7 × 13 × 17 × 19 = 881.790
23 × 3 × 52 × 7 × 13 × 17 = 928.200
23 × 3 × 52 × 7 × 13 × 19 = 1.037.400
23 × 5 × 7 × 13 × 17 × 19 = 1.175.720
22 × 3 × 52 × 13 × 17 × 19 = 1.259.700
23 × 3 × 52 × 7 × 17 × 19 = 1.356.600
2 × 52 × 7 × 13 × 17 × 19 = 1.469.650
22 × 3 × 5 × 7 × 13 × 17 × 19 = 1.763.580
3 × 52 × 7 × 13 × 17 × 19 = 2.204.475
23 × 3 × 52 × 13 × 17 × 19 = 2.519.400
22 × 52 × 7 × 13 × 17 × 19 = 2.939.300
23 × 3 × 5 × 7 × 13 × 17 × 19 = 3.527.160
2 × 3 × 52 × 7 × 13 × 17 × 19 = 4.408.950
23 × 52 × 7 × 13 × 17 × 19 = 5.878.600
22 × 3 × 52 × 7 × 13 × 17 × 19 = 8.817.900
23 × 3 × 52 × 7 × 13 × 17 × 19 = 17.635.800

最终答案:
(向下滚动)

17.635.800 有 384 个除数:
1; 2; 3; 4; 5; 6; 7; 8; 10; 12; 13; 14; 15; 17; 19; 20; 21; 24; 25; 26; 28; 30; 34; 35; 38; 39; 40; 42; 50; 51; 52; 56; 57; 60; 65; 68; 70; 75; 76; 78; 84; 85; 91; 95; 100; 102; 104; 105; 114; 119; 120; 130; 133; 136; 140; 150; 152; 156; 168; 170; 175; 182; 190; 195; 200; 204; 210; 221; 228; 238; 247; 255; 260; 266; 273; 280; 285; 300; 312; 323; 325; 340; 350; 357; 364; 380; 390; 399; 408; 420; 425; 442; 455; 456; 475; 476; 494; 510; 520; 525; 532; 546; 570; 595; 600; 646; 650; 663; 665; 680; 700; 714; 728; 741; 760; 780; 798; 840; 850; 884; 910; 950; 952; 969; 975; 988; 1.020; 1.050; 1.064; 1.092; 1.105; 1.140; 1.190; 1.235; 1.275; 1.292; 1.300; 1.326; 1.330; 1.365; 1.400; 1.425; 1.428; 1.482; 1.547; 1.560; 1.596; 1.615; 1.700; 1.729; 1.768; 1.785; 1.820; 1.900; 1.938; 1.950; 1.976; 1.995; 2.040; 2.100; 2.184; 2.210; 2.261; 2.275; 2.280; 2.380; 2.470; 2.550; 2.584; 2.600; 2.652; 2.660; 2.730; 2.850; 2.856; 2.964; 2.975; 3.094; 3.192; 3.230; 3.315; 3.325; 3.400; 3.458; 3.570; 3.640; 3.705; 3.800; 3.876; 3.900; 3.990; 4.199; 4.200; 4.420; 4.522; 4.550; 4.641; 4.760; 4.845; 4.940; 5.100; 5.187; 5.304; 5.320; 5.460; 5.525; 5.700; 5.928; 5.950; 6.175; 6.188; 6.460; 6.630; 6.650; 6.783; 6.825; 6.916; 7.140; 7.410; 7.735; 7.752; 7.800; 7.980; 8.075; 8.398; 8.645; 8.840; 8.925; 9.044; 9.100; 9.282; 9.690; 9.880; 9.975; 10.200; 10.374; 10.920; 11.050; 11.305; 11.400; 11.900; 12.350; 12.376; 12.597; 12.920; 13.260; 13.300; 13.566; 13.650; 13.832; 14.280; 14.820; 15.470; 15.960; 16.150; 16.575; 16.796; 17.290; 17.850; 18.088; 18.200; 18.525; 18.564; 19.380; 19.950; 20.748; 20.995; 22.100; 22.610; 23.205; 23.800; 24.225; 24.700; 25.194; 25.935; 26.520; 26.600; 27.132; 27.300; 29.393; 29.640; 30.940; 32.300; 33.150; 33.592; 33.915; 34.580; 35.700; 37.050; 37.128; 38.675; 38.760; 39.900; 41.496; 41.990; 43.225; 44.200; 45.220; 46.410; 48.450; 49.400; 50.388; 51.870; 54.264; 54.600; 56.525; 58.786; 61.880; 62.985; 64.600; 66.300; 67.830; 69.160; 71.400; 74.100; 77.350; 79.800; 83.980; 86.450; 88.179; 90.440; 92.820; 96.900; 100.776; 103.740; 104.975; 113.050; 116.025; 117.572; 125.970; 129.675; 132.600; 135.660; 146.965; 148.200; 154.700; 167.960; 169.575; 172.900; 176.358; 185.640; 193.800; 207.480; 209.950; 226.100; 232.050; 235.144; 251.940; 259.350; 271.320; 293.930; 309.400; 314.925; 339.150; 345.800; 352.716; 419.900; 440.895; 452.200; 464.100; 503.880; 518.700; 587.860; 629.850; 678.300; 705.432; 734.825; 839.800; 881.790; 928.200; 1.037.400; 1.175.720; 1.259.700; 1.356.600; 1.469.650; 1.763.580; 2.204.475; 2.519.400; 2.939.300; 3.527.160; 4.408.950; 5.878.600; 8.817.900 和 17.635.800
其中有 7 个质因数: 2; 3; 5; 7; 13; 17 和 19

找到一个数字的所有除数的一种快速方法是将其分解为质因数.

然后在所有不同的组合中乘以质因数及其指数 （如果有的话）.


其他与计算除数类似的操作：

» 数字 17.635.792 的所有除数和质因数是多少？

» 数字 17.635.806 的所有除数和质因数是多少？


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。

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一个或两个数字的所有计算除数的列表

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。