# Power of 5

• December 2nd 2009, 11:57 AM
itsmaximhere
Power of 5
What is the power of 5 in

(1!*2!......10!)*(1!*2!.....100!)*(1!*2!.....1000! )
• December 2nd 2009, 12:13 PM
earboth
Quote:

Originally Posted by itsmaximhere
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 $5^6$

(1!*2!.....100!) contains $5^{96} \cdot (5^2)^{76}$

(1!*2!.....1000!) contains $5^{996} \cdot (5^2)^{976} \cdot (5^3)^{876} \cdot (5^4)^{376}$