The smallest number greater than 200 that has exactly 4 prime factors is 210. This number can be expressed as the product of its prime factors: (2 \times 3 \times 5 \times 7), which indeed yields four distinct prime factors. Other combinations, such as using powers of primes, do not yield a smaller number exceeding 200.
12
I think that it is 4
45
It is 2^6 = 64.
I belive it is 4. The factors of 4 are 1,4, and 2.
The smallest number that has exactly eight factors is 24. The factors of 1,2,3,4,6,8,12, and 24
6
192
6
4096
192
12
I think that it is 4
1024
The smallest number that has exactly three factors is 4.
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.
It is in fact 72