If A=810^n分之810乘811乘812乘...乘2010乘2011 is a positive interger,then the maximum value of positive interger n is(

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If A=810^n分之810乘811乘812乘...乘2010乘2011 is a positive interger,then the maximum value of positive interger n is(
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If A=810^n分之810乘811乘812乘...乘2010乘2011 is a positive interger,then the maximum value of positive interger n is(
If A=810^n分之810乘811乘812乘...乘2010乘2011 is a positive interger,then the maximum value of positive interger n is(

If A=810^n分之810乘811乘812乘...乘2010乘2011 is a positive interger,then the maximum value of positive interger n is(
810=9*9*10=3的4次方*10
设y=810×811×812×813×814×…×2009×2010×2011
需要找810的n次方中10的个数以及3的4n次方数有多少个[2011/3] - [809/3] = 670 - 269 = 401
[670/3] - [269/3] = 223 - 89 = 134
[223/3] - [89/3] = 77 - 29 = 48
[77/3] - [29/3] = 25 - 9 = 16
[25/3] - [9/3] = 8 - 3 = 5
[8/3] - [3/3] = 2 -1 =1
401+134+48+16+5+1=605
也就是说y可以包括605个3相乘
[2011/5] - [809/5] = 402 - 41 = 361
[402/5] - [41/5] = 80 - 8 = 72
[80/5] - [8/5] = 16 - 1 = 15
[16/5] - [1/5] = 3- 0 = 3
361+72+15+3=451
也就是说y可以包括451个5相乘
也就是说3的次方数有605个,5的次方数有451个
求出3的4次方数5的次方数的最小值,min([605/4],451)=150
max(n)=150