这个数有90个因数,能被210整除,这个数是多少
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解决时间 2021-03-29 04:50
- 提问者网友：夢醒日落
- 2021-03-28 21:15
这个数有90个因数,能被210整除,这个数是多少
最佳答案
- 五星知识达人网友：纵马山川剑自提
- 2021-03-28 21:49
能被210=2*3*5*7整除，则因子中必有2，3，5，7的幂，这些幂（都大于0）不妨分别设为a,b,c,d
有90个因数，则
(a+1)(b+1)(c+1)(d+1)=90=2‧3‧3‧5
因此，不妨取
a+1=2
b+1=3
c+1=3
d+1=5
即
a=1,
b=2
c=2
d=4
也即
2*3^2*5^2*7^4=1080450
可以被它的全部因子（共90个） 整除：1,2,3,5,6,7,9,10,14,15,18,21,25,30,35,42,45,49,50,63,70,75,90,98,105,126,147,150,175,210,225,245,294,315,343,350,441,450,490,525,630,686,735,882,1029,1050,1225,1470,1575,1715,2058,2205,2401,2450,3087,3150,3430,3675,4410,4802,5145,6174,7203,7350,8575,10290,11025,12005,14406,15435,17150,21609,22050,24010,25725,30870,36015,43218,51450,60025,72030,77175,108045,120050,154350,180075,216090,360150,540225,1080450
有90个因数，则
(a+1)(b+1)(c+1)(d+1)=90=2‧3‧3‧5
因此，不妨取
a+1=2
b+1=3
c+1=3
d+1=5
即
a=1,
b=2
c=2
d=4
也即
2*3^2*5^2*7^4=1080450
可以被它的全部因子（共90个） 整除：1,2,3,5,6,7,9,10,14,15,18,21,25,30,35,42,45,49,50,63,70,75,90,98,105,126,147,150,175,210,225,245,294,315,343,350,441,450,490,525,630,686,735,882,1029,1050,1225,1470,1575,1715,2058,2205,2401,2450,3087,3150,3430,3675,4410,4802,5145,6174,7203,7350,8575,10290,11025,12005,14406,15435,17150,21609,22050,24010,25725,30870,36015,43218,51450,60025,72030,77175,108045,120050,154350,180075,216090,360150,540225,1080450
全部回答
- 1楼网友：妄饮晩冬酒
- 2021-03-28 22:36
题目错了，是不是能正除210
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