Number Theory

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 ... so. three terminal zeroes.      

_.   

We could multiply these numbers together, but we could also do this. 

$40 \cdot 6 \cdot75\cdot 12 = \\ 40 \cdot6 \cdot[3 \cdot25] \cdot[ 3\cdot4 ] = \\ 40 \cdot 6 \cdot [ 3 \cdot 3 ] \cdot [ 25 \cdot4] = \\ 6 \cdot 40 \cdot 9 \cdot 100 = \\ 54 \cdot 4000 = \\ 54 \cdot 4 \cdot1000 = \\ 216 \cdot10^3$

Thus, there are 3 terminal zeroes. 

Thanks! :)