Divide and conquer

How many distinct prime factors does the following number have?

\[ 20 \times 21 \times 22 \times 23 \times 24 \times 25 \times 26 \times 27 \times 28 \times 29 \times 30 \]

Details and assumptions

The number \( 12 = 2^2 \times 3 \) has 2 distinct prime factors, namely 2 and 3.

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