There are infinitely many such numbers.
If p is a prime then p^11 has 12 factors.
If p and q are any two primes, then p*q^5 has 12 factors.
If p and q are any two primes, then p^2*q^3 has 12 factors.
If p, q and r are any three primes, then p*q*r^2 has 12 factors.
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