# Factorial Base 4

Let $$N$$ be the number of digits of $$\large {\dfrac{(1000_4)!}{(332_4)!}}$$ in base 4. Find $$N$$.

Notations:

• $$!$$ represents the factorial notation.

• $$a_b$$ means $$a$$ base $$b$$. The numbers in the problem above are in base 4.

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