Answer: Option D
:
D
Note that 71! has 16 zeroes at its end.(You can find this out by finding the highest power of 5 in 71!)
So does 70!.
66! To 69! Have 15 zeroes at its end. Multiplication of these itself amounts to $>202$
Hence the ${202}^{nd}$ digit is 0
To find the highest power of a number in a factorial
a)Highest power of a prime number in a factorial:
To find the highest power of a prime number (x) in a factorial (N!), continuously divide N by x and add all the quotients.
Eg) Find the highest power of 100!
Solution:
$\frac{100}{5}=20;\frac{20}{5}=4;$
Adding the quotients, its 20+4=24. So highest power of 5 in 100! = 24
b)Highest number of a composite number in factorial
1)Factorize the number into primes.
2)Find the highest power of all the prime numbers in that factorial using the previous method.
3)Take the least power.