Question

Let f(n) be a function that, given an integer n, returns an integer k, where k is the smallest possible integer such that k! is divisible by n. Given that n is a multiple of 15, what is the smallest value of n such that f(n)>15?

a) 45
b) 30
c) 60
d) 75

Answer 1

The smallest value of n such that f(n) > 15 is n = 5.

Step-by-step explanation:

To find the smallest value of n such that f(n) > 15, we need to understand how f(n) is calculated. Given that n is a multiple of 15, we know that the smallest value of n is 15. Now we need to find the smallest k such that k! is divisible by 15.

The factorial function (k!) is the product of all positive integers from 1 to k. To find the smallest k such that k! is divisible by 15, we can test different values of k starting from 1 until we find a k for which k! is divisible by 15.

Testing k = 1, we find that 1! = 1 which is not divisible by 15. Testing k = 2, we find that 2! = 2 which is also not divisible by 15. Continuing this process, we find that the smallest k for which k! is divisible by 15 is k = 5. Therefore, the smallest value of n such that f(n) > 15 is n = k = 5.