Find the last non zero digit of 28!. 
Find the last non zero digit of 28!.

It is very hard to multiply and find the last nonzero digit. I just wanna know that, is there any easy technique to solve this type of problem?

Note that
$$5\times 10\times 15\times 20\times 25=5\times(2\cdot 5)\times (3\cdot 5)\times (2^2\cdot 5)\times 5^2=2^3\cdot 3\cdot 5^6$$
and that 
$$10^6=2^6\cdot 5^6=\frac{8\cdot 5\cdot 10\cdot 15\cdot 20\cdot 25}{3}=8\cdot 5\cdot 10\cdot 5\cdot 20\cdot 25.$$
So, in mod $10$, we have
$$\begin{align}\frac{28!}{10^6}&\equiv 1\cdot 2\cdot 3\cdot 4\cdot 6\cdot 7\cdot 9\cdot 1\cdot 2\cdot 3\cdot 4\cdot 3\cdot 6\cdot 7\cdot 8\cdot 9\cdot 1\cdot 2\cdot 3\cdot 4\cdot 6\cdot 7\cdot 8\\&\equiv (1\cdot 2\cdot 3\cdot 4\cdot 6\cdot 7)^3\cdot 3\cdot 8^2\cdot 9^2\\&\equiv \{1\cdot 2\cdot 3\cdot 4\cdot (-4)\cdot (-3)\}^3 \cdot 3\cdot 4\cdot 1\\&\equiv 2\cdot 2\\&\equiv 4.\end{align}$$
