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?
The numbers $72, 8, 24, 10, 5, 45, 36, 15$ are grouped in pairs so that each pair has the same product. Which number is paired with $10$?
If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.