What is the power of 5 in
(1!*2!......10!)*(1!*2!.....100!)*(1!*2!.....1000! )
Analyze the number of factor 5 in the brackets:
(1!*2!......10!) contains $\displaystyle 5^6$
(1!*2!.....100!) contains $\displaystyle 5^{96} \cdot (5^2)^{76}$
(1!*2!.....1000!) contains $\displaystyle 5^{996} \cdot (5^2)^{976} \cdot (5^3)^{876} \cdot (5^4)^{376}$
Not sure about the last line so check my arithmetic, please!