Few Questions on Number Theory and Counting (combined)

CAT has been consistently asking questions combining basic number theory and counting. So, it is probably good practice to have a go at these.

1. From the digits 2,3,4,5,6 and 7, how many 5-digit numbers can be formed that have distinct digits and are multiples of 12?

2. All numbers from 1 to 200 (in decimal system) are written in base 6 and base 7 systems. How many of the numbers will have a non-zero units digit in both base 6 and base 7 notations?

3. All numbers from 1 to 150 (in decimal system) are written in base 6 notation. How many of these will not contain any zero?

4. How many factors of 1080 are perfect squares?

Solutions to these questions can be found here.