A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

eramsby1O1O Jul 7, 2024

#1**0 **

If a number is written in the form of \(p_1^a p_2^bp_3^c...\), where all p's are prime numners, it will have (a+1)(b+1)(c+1)... factors. Therefore, a terrific number must be writen in the form of either \(p^9\), or \(p_1^1p_2^4\). The smallest possibilities for each respectively are 2^9 or 512 and 3(2^4) or 48. Therefore, **48 is the smallest terrific number**.

Maxematics Jul 7, 2024