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A Biggy

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 power.

Why 24?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Factoring a Million

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Three Primes

Age 14 to 16 Short
Challenge Level

How many sets of three prime numbers have the property that the product of the three numbers is exactly five times their sum? (The order of the three numbers is not important).

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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.