Find the smallest positive integer N such that N/2 is a perfect
cube, N/3 is a perfect fifth power and N/5 is a perfect seventh
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
This problem is taken from the UKMT Mathematical Challenges.