A positive integer is called terrific if it has exactly 5 positive divisors. What is the largest number of primes that could divide a terrific positive integer?

Hi6942O Jun 23, 2024

#1**+1 **

to get the number of divisors an integer has we multiply the powers of the primes +1. for example 20 is 2^2*5^1 so the total number of divisors is (2+1)(1+1) or 6. so we need to reverse this process for 5. 5 is prime so it has to be 1*5 or p^4. there can only be \(\boxed 1\) prime that divides a terrific positive integer. so much for being terrific ;P

shmewy Jun 23, 2024