答案：439
1*2*...*439乘積為：
127953292353780418662295882096174208729627838634368275703626696167481934088949078478422414966082866398234140870473493172222347061821170297377391062536948648247440240125365857997650107720992645698342045851453491013937341603408773310840584017280282347869728321579198052566281827734291973919449640935452430089168997338555943074357078723442098245363530979944906801747788998369749832525367550179846512404738651425605334348108461520593686446263050766220502589566034021786770175890463101709873617585422105287162659434170578492937629698321512117234595605280550570528930600694361524608390506050805586040233494883658352768693356191148563251400156876455027117283705050962639953456110965460027317912091752229061918540881372078145837743756194853014034232349281023688213103609103281042586792765352550544989370989321229076818081185146202642249018014637512801315909196874410413260800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
乘到440就有108個0了.
可以這樣分析,
0的數(shù)目就是包含多少個10,10由2*5得到,在階乘中,因子2明顯比5多,所以問題簡化為：
1*2*...*n可以表達(dá)成5^107*a,a不包含因子5時(shí),n最大多大.
然后就可以數(shù)因子了,5,10,15,20,25,...
包含因子5數(shù)分別為1,1,1,1,2,...
把下面的數(shù)字加起來得到108的時(shí)候,你發(fā)現(xiàn)數(shù)到440了,
所以107個0是439最大,
不知道你是什么年級?
能不能理解?