Question

Find the 202^nd digit from the right in the product of 4! x 5! x 6!...............71!?

• A. 1
• B. 2
• C. 3
• D. 0
• E. 4

Answer 1

The correct option is D 0

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:

100/5=20; 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.