The smallest is 192 but there are infinitely many such numbers. For example, take any Prime number to the 13th power and the result will have exactly fourteen factors. The smallest is 192.
14
192
A prime number has exactly two factors.
A number has exactly three factors if and only if it is the square of a prime number.
36 has 9 factors.
14
The first with exactly 14 is 192.
192
192
Their common factors are 1 and 7 .
A prime number has exactly two factors.
Prime factorizations are unique. No other number will have exactly the same number of prime factors as 28. Multiples of 14 will have some of the same factors.
The smallest number with exactly eight factors is 24.
Well, If we looked at this way: (224) = 16777216, so this number has exactly 24 factors. (324) = 282429536481, so this number has exactly 24 factors. (510)(210)(34) = 810000000000, so this number has exactly 24 factors.
A number has exactly three factors if and only if it is the square of a prime number.
A prime number has exactly two factors: 1 and itself.
A prime number is a whole number with exactly two factors: 1 and itself.