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I'm Eight

Find a great variety of ways of asking questions which make 8.

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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.

Thirty Six Exactly

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

The number $12 = 2^2 \times 3$ has 6 factors. What is the smallest natural number with exactly 36 factors?