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.

Stage: 3 Challenge Level:

$23 \times 21$ is the same as

$$(20 \times 21) + (3 \times 21)$$

which is the same as

$$((20 \times 20) + (20 \times 1)) + ((3 \times 20) + (3 \times 1))$$

Can you figure out where each of these four products appears in the different methods?

Can you deconstruct $246 \times 34$ in the same way?