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Find the number of zeros at the end in p...

Find the number of zeros at the end in product `5^6 .6^7 .7^8 .8^9 .9^(10) .30^(31)` .

Text Solution

Verified by Experts

Given product
`P=5^(6).6^(7).7^(8)..(30)^(31)`
`=[(5)^(6)(10)^(11)(15)^(16)(20)^(21)(25)^(26)(30)^(31)]lamda " " ("where" lamda " is an integer")`
`therefore` Exponent of 5 in P=6+11+16+21+2(26)+31=137
`therefore` Number of zeros =137
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