题目

23760的因数有哪些?已知A既是23760的因数,又是11的倍数,问这样的A有几个?

提问时间：2020-12-21

答案

23760 = 2^4 * 3^3 * 5 * 11
23760的因数有 (4+1)*(3+1)*(1+1)*(1+1)=5*4*2*2 = 80个,分别是：
1,2,3,4,5,6,8,9,
10,11,12,15,16,18,20,22,
24,27,30,33,36,40,44,45,
48,54,55,60,66,72,80,88,
90,99,108,110,120,132,135,144,
165,176,180,198,216,220,240,264,
270,297,330,360,396,432,440,495,
528,540,594,660,720,792,880,990,
1080,1188,1320,1485,1584,1980,2160,2376,
2640,2970,3960,4752,5940,7920,11880,23760
A既是23760的因数,又是11的倍数,则23760除以11= 2^4 * 3^3 * 5
A有(4+1)*(3+1)*(1+1) = 5*4*2=40种可能,A可以是：
11,22,33,44,55,66,88,99,
110,132,165,176,198,220,264,297,
330,396,440,495,528,594,660,792,
880,990,1188,1320,1485,1584,1980,2376,
2640,2970,3960,4752,5940,7920,11880,23760,