+900 A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?
+135 If you have a number in the form of pn where p is a prime number, it will have n + 1 factors. Therefore 29 or 512 will have 10 factors (1, 2, 4, 8, 16, 32, 64, 128, 256, 512), but 2 will be the only prime number that it is divisible by. This is also true for 39 (19683), 59 (1953125), 79 (40353607), or any number in the form of p9, where p is a prime number. Therefore, one prime number is the minimum number of factors for a terrific number.
