How do I know if the number is divisible by $60$? I was study Babel Civilization ( Babylon ) , I see what about the number $60$ now I'm going to find a trick or fast method to know the rest of divisibility by number $60$ for example : 
$6689=60^{2}+51.60+29$ 
$2567=42.60+47$ 
I know that the number $60$ divisible by $1,2,3,4,5,6$ 
So I need fast know method I mean how the rest ? 
I don't if we can generalized or no ? 
Please I need fast method without using calculator !
For example $17894=?$ 
See that : $2177,12=2177+0,12$ 
$2177=36.60+17$
$0,12=\frac{3}{25}=\frac{60.3}{25.60}=?$ 
I need written in base $60$ ?

Being divisible to $60$ is equivalent to being divisible simultaneously to $3,20$. So we can use divisibility test for these, which are easy in base $10$. Divisibility by $20$ mean the last $2$ digits must be and even number followed by $0$. Divisibility by $3$ mean sum of digits is divisible by $3$.
