Find the quotient when total no. Of divisors of 16! is divided by right most non-zero digit of 15! Choices
A) 672  B) 682  C) 692  D) 745  E) 845

Rationale: first find the factors of 16 ! and then divide with non zero digit of 15 ! factors of 16 ! prime no below 16 are 2 3 5 7 11 13 now highest power of 2 in 16 ! is 15 3 is 65 is 37 is 211 , is 113 is 1 so no of factors is 16 * 7 * 4 * 3 * 2 * 2 = 5376 now last digit in 15 ! it can be written as 2 ^ 11 * 3 ^ 6 * 5 ^ 3 * 7 ^ 2 * 11 ^ 1 * 13 * 1 5 ^ 3 * 2 ^ 3 gives 0 so remaining is 2 ^ 3 = 8 therefore 5376 / 8 = 672 answer : a
Answer: A