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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.

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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.

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Factoring a Million

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


Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
Lyndon explains why this is one of his favourite NRICH problems.

I like the twist that means you need to take a little care - you need to worry about detail.

Although it uses factorial notation, this is only a very minor part of the problem- basically it means you can make your point succinctly - that is what mathematical notation is all about.

Possible extension.
My additional question of how many zeros also points out that an apparently closed problem can be easily opened up, with further questions to be asked.

This problem is a special case of Factorial Fun.

Possible support
See also Powerful Factorial and Factoring Factorials which are also special cases.