Number Theory

40 = 5 * 2^3 

6 = 2 * 3

75 = 5 ^2 * 3

12 = 2^2 * 3

 

We have three 5s, and definitely more than three 2s. Thus we have 3 terminal zeros. (remember, 5 * 2 = 10). 

 

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?    

 

40 • 6 • 75 • 12 = 216,000     Three    

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