I'm Eight

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

Repeaters

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.

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:

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