What is the smallest number with exactly 14 divisors?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Colin has a collection of more than $24$ coins. When he puts the coins in piles of $6$, there are $3$ coins remaining. When he puts the coins in piles of $8$, there are $7$ coins remaining. How many coins remain when he puts the coins in piles of $24$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.