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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?


Age 14 to 16 Challenge Level:

If factorial $100$ ($100!$) was rewritten as the product of its prime factors how many $2$s and how many $5$s would there be?
Along the way, confirm how many zeros are at the end of this large number and what the first digit to precede them is.

In the Teachers' Resources, Lyndon explains why he likes this problem.