3 x 5 x 7 = 105
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The only two-digit number that has three different prime factors is 2 x 3 x 5, which equals 30. This number has the prime factors 2, 3, and 5, all of which are distinct prime numbers. Any other two-digit number with three prime factors would have at least one repeated prime factor, making it not have three different prime factors.
Using prime factorization, there are 2 three digit numbers with 9 factors: 512 and 768. There are no three digit numbers with 10 or more prime factors. 512=2^9 and 768=3*2^8
The smallest three digit prime number is 101.
800 2x2x2x2x2x5x5
If you're asking about distinct prime factors, there are eight numbers tied with three of them. If not, 64 has six twos.