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14 Divisors

What is the smallest number with exactly 14 divisors?

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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.

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Oh! Hidden Inside?

Find the number which has 8 divisors, such that the product of the divisors is 331776.


Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

I used a spreadsheet to get the sense of what was happening. It is easy to see the pattern but the question is asking you to try to explain it!