Question Number 2387 by prakash jain last updated on 18/Nov/15
$$\mathrm{How}\:\mathrm{many}\:\mathrm{0}{s}\:\mathrm{at}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{1000}!? \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{first}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{digits}\:\mathrm{from}\:\mathrm{the}\:\mathrm{right}? \\ $$
Commented by prakash jain last updated on 18/Nov/15
$$\mathrm{Number}\:\mathrm{of}\:\mathrm{zero}\:\mathrm{can}\:\mathrm{be}\:\mathrm{computed}\:\mathrm{using} \\ $$$$\frac{\mathrm{1000}}{\mathrm{5}}+\frac{\mathrm{1000}}{\mathrm{25}}+\frac{\mathrm{1000}}{\mathrm{125}}+\frac{\mathrm{1000}}{\mathrm{625}}=\mathrm{249} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{appropriate}\:\mathrm{method}\:\mathrm{for}\:\mathrm{computing} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{digit}? \\ $$
Commented by Yozzi last updated on 18/Nov/15
$${What}\:{is}\:'\mathrm{1000}!?'\:?\:{Is}\:{it}\:'\mathrm{1000}!\:\:?'\:? \\ $$
Commented by prakash jain last updated on 19/Nov/15
$$\mathrm{1000}\:{factorial}. \\ $$
Commented by RasheedAhmad last updated on 19/Nov/15
![According to calculation of Mr prakash jain there are 249 zeros on the right of 1000! Then what about 250^(th) digit Will this not be nonzero [?] If I am right then First determine number of zeros ,if this is k then (k+1)^(th) digit is nonzero from right.](Q2420.png)
$${According}\:{to}\:{calculation}\:{of} \\ $$$${Mr}\:{prakash}\:{jain}\:{there}\:{are}\:\mathrm{249} \\ $$$${zeros}\:{on}\:{the}\:{right}\:{of}\:\mathrm{1000}! \\ $$$${Then}\:{what}\:{about}\:\mathrm{250}^{{th}} \:{digit} \\ $$$${Will}\:{this}\:{not}\:{be}\:{nonzero}\:\left[?\right] \\ $$$${If}\:{I}\:{am}\:{right}\:{then}\: \\ $$$${First}\:{determine}\:{number}\:{of} \\ $$$${zeros}\:,{if}\:{this}\:{is}\:{k}\:{then}\:\left({k}+\mathrm{1}\right)^{{th}} \\ $$$${digit}\:{is}\:{nonzero}\:{from}\:{right}. \\ $$