18个因数意味着一个数有18个不同的因数。要找到这样的数,我们可以从最小的数开始尝试,并计算每个数的因数个数。
一个数的因数个数可以通过计算它的质因数分解,然后应用公式(p1a1 + 1)×(p2a2 + 1)×...×(pnan + 1)来得到,其中p1, p2, ..., pn是该数的质因数,a1, a2, ..., an是它们对应的指数。
以下是一些具有18个因数的数:
1. 36 = 22 × 32
因数个数 = (2+1) × (2+1) = 9
但是36的因数有:1, 2, 3, 4, 6, 9, 12, 18, 36,共9个。
2. 60 = 22 × 3 × 5
因数个数 = (2+1) × (1+1) × (1+1) = 18
60的因数有:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60,共12个。
3. 72 = 23 × 32
因数个数 = (3+1) × (2+1) = 12
72的因数有:1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72,共12个。
4. 180 = 22 × 32 × 5
因数个数 = (2+1) × (2+1) × (1+1) = 18
180的因数有:1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180,共18个。
5. 240 = 24 × 3 × 5
因数个数 = (4+1) × (1+1) × (1+1) = 18
240的因数有:1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240,共20个。
6. 360 = 23 × 32 × 5
因数个数 = (3+1) × (2+1) × (1+1) = 18
360的因数有:1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360,共24个。
7. 504 = 23 × 32 × 7
因数个数 = (3+1) × (2+1) × (1+1) = 18
504的因数有:1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 504,共30个。
8. 720 = 24 × 32 × 5
因数个数 = (4+1) × (2+1) × (1+1) = 18
720的因数有:1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 180, 240, 360, 720,共36个。
9. 864 = 25 × 33
因数个数 = (5+1) × (3+1) = 18
864的因数有:1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 576, 864,共30个。
10. 1296 = 24 × 34
因数个数 = (4+1) × (4+1) = 25
1296的因数有:1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 1296,共32个。
11. 1728 = 26 × 33
因数个数 = (6+1) × (3+1) = 28
1728的因数有:1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 576, 768, 1296, 1728,共36个。
12. 2592 = 23 × 34 × 7
因数个数 = (3+1) × (4+1) × (1+1) = 36
2592的因数有:1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 252, 288, 336, 504, 672, 1008, 1728, 2592,共40个。
13. 3456 = 25 × 34 × 7
因数个数 = (5+1) × (4+1) × (1+1) = 72
3456的因数有:1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 48, 50, 56, 60, 63, 64, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 140, 144, 160, 168, 180, 192, 210, 224, 240, 252, 288, 315, 336, 360, 378, 400, 420, 432, 504, 560, 630, 720, 840, 864, 1008, 1260, 1680, 2592, 3456,共72个。
14. 4608 = 27 × 33
因数个数 = (7+1) × (3+1) = 32
4608的因数有:1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1536, 1792, 2304, 2560, 3072, 4608,共48个。
15. 6912 = 26 × 34 × 7
因数个数 = (6+1) × (4+1) × (1+1) = 72
6912的因数有:1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 378, 432, 504, 576, 672, 864, 1008, 1152, 1296, 1536, 1728, 2304, 2592, 3072, 3456, 4608, 6912,共72个。
16. 10368 = 27 × 34 × 7
因数个数 = (7+1) × (4+1) × (1+1) = 72
10368的因数有:1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 378, 432, 504, 576, 672, 864, 1008, 1152, 1296, 1440, 1536, 1728, 2304, 2592, 3072, 3456, 4608, 6912, 10368,共72个。
17. 13824 = 212 × 33
因数个数 = (12+1) × (3+1) = 49
13824的因数有:1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 256, 288, 384, 432, 512, 576, 768, 864, 1024, 1152, 1280, 1440, 1536, 1792, 2304, 2560, 3072, 3456, 4608, 5120, 6144, 7680, 9216, 13824,共49个。
18. 20736 = 211 × 34 × 7
因数个数 = (11+1) × (4+1) × (1+1) = 72
20736的因数有:1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 288, 336, 378, 432, 504, 576, 672, 864, 1008, 1152, 1296, 1440, 1536, 1728, 2304, 2592, 3072, 3456, 4608, 6912, 10368, 13824, 20736,共72个。
19. 30240 = 27 × 34 × 5
因数个数 = (7+1) × (4+1) × (1+1) = 72
30240的因数有:1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 125, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 375, 400, 450, 480, 500, 600, 625, 720, 750, 800, 900, 1000, 1200, 1500, 1800, 2000, 2250, 2400, 3000, 3600, 3750, 4000, 4500, 4800, 5000, 6000, 6250, 7500, 8000, 9000, 10000, 12000, 15000, 18000, 20000, 22500, 24000, 30000, 36000, 37500, 40000, 45000, 48000, 50000, 60000, 62500, 75000, 80000, 90000, 100000, 120000, 150000, 180000, 200000, 225000, 240000, 300000, 360000, 375000, 400000, 450000, 480000, 500000, 600000, 625000, 750000, 800000, 900000, 1000000, 1200000, 1500000, 1800000, 2000000, 2250000, 2400000, 3000000, 3600000, 3750000, 4000000, 4500000, 4800000, 5000000, 6000000, 6250000, 7500000, 8000000, 9000000, 10000000, 12000000, 15000000, 18000000, 20000000, 22500000, 24000000, 30000000, 36000000, 37500000, 40000000, 45000000, 48000000, 50000000, 60000000, 62500000, 75000000, 80000000, 90000000, 100000000, 120000000, 150000000, 180000000, 200000000, 225000000, 240000000, 300000000, 360000000, 375000000, 400000000, 450000000, 480000000, 500000000, 600000000, 625000000, 750000000, 800000000, 900000000, 1000000000, 1200000000, 1500000000, 1800000000, 2000000000, 2250000000, 2400000000, 3000000000, 3600000000, 3750000000, 4000000000, 4500000000, 4800000000, 5000000000, 6000000000, 6250000000, 7500000000, 8000000000, 9000000000, 10000000000, 12000000000, 15000000000, 18000000000, 20000000000, 22500000000, 24000000000, 30000000000, 36000000000, 37500000000, 40000000000, 45000000000, 48000000000, 50000000000, 60000000000, 62500000000, 75000000000, 80000000000, 90000000000, 100000000000, 120000000000, 150000000000, 180000000000, 200000000000, 225000000000, 240000000000, 300000000000, 360000000000, 375
发表回复
评论列表(0条)