The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 70 and n is not prime, what is the greatest possible value of f(n)?  Choose the correct choice from the following answers: A) 68 B) 65 C) 62 D) 60 E) 55
Since we need the largest value of f (n), we will start with the largest option.   Option A: 68 = 2*2*17. This is not a product of distinct prime numbers. Hence incorrect   Option B: 65 = 5*13. This is a product of distinct prime numbers.   Rest all the options are smaller that 65.   Correct Option: 65
<result>B</result>
The function f is defined for all positive integers n by the following rule: f(n) is the product of the distinct prime factors of n. If f(n) < 70 and n is not prime, what is the greatest possible value of f(n)?