# Divide and conquer

Number Theory Level 2

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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