SOLUTION: what is the smallest number divisible by 10 and such that the factorial of this number is divisible by 10共 ? a) 40 b) 50 c) 60 d) 80 e) 100

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Question 1055461: what is the smallest number divisible by 10 and such that the factorial of this number is divisible by 10共 ?
a) 40 b) 50 c) 60 d) 80 e) 100
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
what is the smallest number divisible by 10 and such that the factorial of this number is divisible by 10共 ?
a) 40 b) 50 c) 60 d) 80 e) 100
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TABLE

The number n         5    10   15   20    25   30   40   45   50    55    60

n! is divisible by   5^1  5^2  5^3  5^4   5^6  5^7  5^8  5^9  5^11  5^12  5^13


The Table shows that  5! is divisible by 5 in degree 1.
                     10! is divisible by 5 in degree 2.
                     15! is divisible by 5 in degree 3,  and so on.

Answer. n=55. There is no such an option in your list.


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