Two questions on finding trailing digits in (large) numbers and one on divisibility

Without using a calculator, how can we solve the following?

1. How do we find the number of zeros at the end of $600!$


2. What are the last 3-digits of $171^{172}$?


3. What is the sum of all positive numbers less than or equal to $61$, which are divisible by $3$ as well as by $5$?