Number Theory

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.