To find the number of terminal zeroes in the product $40 \cdot 6 \cdot 75 \cdot 12$, we need to determine how many factors of $10$ are in the product.
$40$ can be written as $2^3 \cdot 5^1$, $6$ as $2^1 \cdot 3^1$, $75$ as $3^1 \cdot 5^2$, and $12$ as $2^2 \cdot 3^1$.
Multiplying these together we get:
$(2^3 \cdot 5^1) \cdot (2^1 \cdot 3^1) \cdot (3^1 \cdot 5^2) \cdot (2^2 \cdot 3^1) = 2^6 \cdot 3^3 \cdot 5^3$
This product has a total of $3$ factors of $5$, so it has $3$ terminal zeroes.
A terminal zero is a $0$ that appears at the end of a number. For example, the number $3,800$ has two terminal zeros.
How many terminal zeroes does $40 \cdot 6 \cdot 75 \cdot 12$ have?
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