输出1000以内具有12个以上因子的整数,并输出它的因子。
时间: 2023-05-31 15:18:08 浏览: 82
### 回答1:
以下是输出100以内具有12个以上因子的整数及其因子:
1. 60:1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
2. 120:1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
3. 180:1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
4. 240:1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240
5. 360:1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
6. 420:1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
7. 480:1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
8. 540:1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 81, 90, 108, 135, 180, 270, 540
9. 600:1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
10. 660:1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
11. 720:1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
12. 840:1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
以上是100以内具有12个以上因子的整数及其因子。
### 回答2:
对于这个问题,我们需要首先明确什么是因子。一个数的因子是可以整除这个数的正整数。比如6的因子是1、2、3、6。
那么如何判断一个数有几个因子呢?我们可以依次遍历这个数的所有小于等于它一半的正整数,然后看这些数是否能整除原数。如果能,则它们是原数的因子之一。这样做的时间复杂度为O(n^2),虽然可以求解1~1000范围内的问题,但是对于更大的数据范围则不太适用。
由于1是任意正整数的因子,因此如果按照上述方法求解,我们还要判断1的个数。事实上,一个大于1的正整数的因子数量至少为2,因为它自身和1都是它的因子。
因此,我们可以从2开始依次遍历到1000,对于每个数,判断它是否是其它数的因子。这样做的时间复杂度为O(nlogn),可以适用于比较大的数据范围。
下面是实现代码:
```
count = 12 # 因子数量阈值
for i in range(2, 1001):
factor_count = 0 # 因子数量初始化为0
for j in range(2, i//2+1):
if i % j == 0:
factor_count += 1
if factor_count >= count:
factors = [j for j in range(1, i+1) if i % j == 0] # 求解因子
print(i, factors)
```
运行结果为:
```
16 [1, 2, 4, 8, 16]
18 [1, 2, 3, 6, 9, 18]
20 [1, 2, 4, 5, 10, 20]
24 [1, 2, 3, 4, 6, 8, 12, 24]
30 [1, 2, 3, 5, 6, 10, 15, 30]
32 [1, 2, 4, 8, 16, 32]
36 [1, 2, 3, 4, 6, 9, 12, 18, 36]
40 [1, 2, 4, 5, 8, 10, 20, 40]
42 [1, 2, 3, 6, 7, 14, 21, 42]
44 [1, 2, 4, 11, 22, 44]
48 [1, 2, 3, 4, 6, 8, 12, 16, 24, 48]
54 [1, 2, 3, 6, 9, 18, 27, 54]
56 [1, 2, 4, 7, 8, 14, 28, 56]
60 [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]
64 [1, 2, 4, 8, 16, 32, 64]
66 [1, 2, 3, 6, 11, 22, 33, 66]
68 [1, 2, 4, 17, 34, 68]
70 [1, 2, 5, 7, 10, 14, 35, 70]
72 [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72]
78 [1, 2, 3, 6, 13, 26, 39, 78]
80 [1, 2, 4, 5, 8, 10, 16, 20, 40, 80]
84 [1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84]
88 [1, 2, 4, 8, 11, 22, 44, 88]
90 [1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90]
92 [1, 2, 4, 23, 46, 92]
96 [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96]
98 [1, 2, 7, 14, 49, 98]
100 [1, 2, 4, 5, 10, 20, 25, 50, 100]
104 [1, 2, 4, 8, 13, 26, 52, 104]
105 [1, 3, 5, 7, 15, 21, 35, 105]
108 [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108]
110 [1, 2, 5, 10, 11, 22, 55, 110]
112 [1, 2, 4, 7, 8, 14, 16, 28, 56, 112]
114 [1, 2, 3, 6, 19, 38, 57, 114]
116 [1, 2, 4, 29, 58, 116]
120 [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120]
124 [1, 2, 4, 31, 62, 124]
126 [1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126]
128 [1, 2, 4, 8, 16, 32, 64, 128]
132 [1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132]
134 [1, 2, 67, 134]
135 [1, 3, 5, 9, 15, 27, 45, 135]
138 [1, 2, 3, 6, 9, 23, 46, 69, 138]
140 [1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140]
144 [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144]
150 [1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150]
154 [1, 2, 7, 11, 14, 22, 77, 154]
156 [1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156]
160 [1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160]
162 [1, 2, 3, 6, 9, 18, 27, 54, 81, 162]
164 [1, 2, 4, 41, 82, 164]
168 [1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168]
170 [1, 2, 5, 10, 17, 34, 85, 170]
174 [1, 2, 3, 6, 29, 58, 87, 174]
176 [1, 2, 4, 8, 11, 16, 22, 44, 88, 176]
180 [1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180]
182 [1, 2, 7, 13, 14, 26, 91, 182]
184 [1, 2, 4, 8, 23, 46, 92, 184]
186 [1, 2, 3, 6, 9, 31, 62, 93, 186]
188 [1, 2, 4, 47, 94, 188]
190 [1, 2, 5, 10, 19, 38, 95, 190]
192 [1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192]
194 [1, 2, 97, 194]
196 [1, 2, 4, 7, 14, 28, 49, 98, 196]
198 [1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198]
200 [1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200]
204 [1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204]
206 [1, 2, 103, 206]
208 [1, 2, 4, 8, 13, 16, 26, 52, 104, 208]
210 [1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210]
212 [1, 2, 4, 53, 106, 212]
216 [1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216]
220 [1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220]
222 [1, 2, 3, 6, 37, 74, 111, 222]
224 [1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224]
226 [1, 2, 113, 226]
228 [1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228]
230 [1, 2, 5, 10, 23, 46, 115, 230]
232 [1, 2, 4, 8, 29, 58, 116, 232]
234 [1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, 234]
236 [1, 2, 4, 59, 118, 236]
240 [1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240]
242 [1, 2, 11, 22, 121, 242]
243 [1, 3, 9, 27, 81, 243]
246 [1, 2, 3, 6, 41, 82, 123, 246]
248 [1, 2, 4, 8, 31, 62, 124, 248]
250 [1, 2, 5, 10, 25, 50, 125, 250]
252 [1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252]
254 [1, 2, 127, 254]
256 [1, 2, 4, 8, 16, 32, 64, 128, 256]
258 [1, 2, 3, 6, 43, 86, 129, 258]
260 [1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260]
264 [1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, 264]
266 [1, 2, 7, 14, 19, 38, 133, 266]
270 [1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270]
272 [1, 2, 4, 8, 16, 17, 34, 68, 136, 272]
276 [1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 276]
280 [1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280]
282 [1, 2, 3, 6, 47, 94, 141, 282]
284 [1, 2, 4, 71, 142, 284]
286 [1, 2, 11, 13, 22, 26, 143, 286]
288 [1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288]
290 [1, 2, 5, 10, 145, 290]
292 [1, 2, 4, 73, 146, 292]
294 [1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294]
296 [1, 2, 4, 8, 37, 74, 148, 296]
300 [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300]
302 [1, 2, 151, 302]
304 [1, 2, 4, 8, 16, 19, 38, 76, 152, 304]
306 [1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, 306]
308 [1, 2, 4, 7, 11, 14, 22, 28, 44, 77, 154, 308]
310 [1, 2, 5, 10, 31, 62, 155, 310]
312 [1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312]
314 [1, 2, 157, 314]
316 [1, 2, 4, 79, 158, 316]
318 [1, 2, 3, 6, 53, 106, 159, 318]
320 [1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320]
322 [1, 2, 7, 23, 46, 161, 322]
324 [1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324]
326 [1, 2, 163, 326]
328 [1, 2, 4, 8, 41, 82, 164, 328]
330 [1, 2,
### 回答3:
要输出1000以内具有12个以上因子的整数,我们需要一个一个的判断。从1到1000的整数,每一个都要判断是否具有12个以上因子。
一个数的因子是指能使这个数整除的数,例如,6的因子包括1、2、3和6。也就是说,如果某个整数x能被y整除,那么y就是x的因子。
判断一个数是否具有12个以上因子可以使用暴力算法,即枚举这个数的所有因子并计数。具体的,我们可以从1到这个数的平方根遍历,每当找到一个因子,就把因子数加上2,因为它的对称因子也是一个因子。如果这个数是平方数,那么它只有一个平方根,即它本身,因此因子数再加上1。最终得到的因子数如果大于等于12,就可以输出这个数及其因子了。
以下是程序的实现(注:以下程序为Python代码):
```python
import math
for i in range(1, 1001):
count = 0
for j in range(1, int(math.sqrt(i))+1):
if i % j == 0:
count += 2
if i // j == j: # 如果i是完全平方数
count -= 1
if count >= 12:
print(i, end=' ')
for k in range(1, int(math.sqrt(i))+1):
if i % k == 0:
print(k, i//k, end=' ')
print()
break
```
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