What is the smallest number with exactly 14 divisors?
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?
For a positive integer $n$, we define $n!$ to be the product of all the positive integers from $1$ to $n$; that is $n!=1\times 2\times 3\times\ldots\times n$. If $n!=2^{15}\times 3^6\times 5^3\times 7^2\times 11\times 13$, what is the value of $n$? 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.