+0  
 
0
1
2
avatar+729 

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?

 Jul 7, 2024
 #2
avatar+88 
0

If you have a number in the form of \(p^n\) where p is a prime number, it will have n + 1 factors. Therefore \(2^9\) 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 \(3^9\) (19683), \(5^9\) (1953125), \(7^9\) (40353607), or any number in the form of \(p^9\), where p is a prime number. Therefore, one prime number is the minimum number of factors for a terrific number.

 Jul 7, 2024

3 Online Users

avatar
avatar
avatar