Find a great variety of ways of asking questions which make 8.
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.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Example 1: Divide by 4 and select all the numbers in the right-hand column - they should all turn red. Now divide by 5 and select all the numbers in the right-hand column - they should all turn yellow, but some will turn orange. What is special about the numbers that turn orange? Now divide by 3 and select all the numbers in the right-hand column - most should turn blue, but one will turn black. What is special about the number that turns black? What is special about the numbers that turn green and purple?
Example 2: (you will need to clear your previous work) Find the numbers that have a remainder of 2 when divided by 5 - you'll need to divide by 5 and select the numbers in the second column. Now select the numbers that have a remainder of 1 when divided by 2 (the odd numbers). What is special about the numbers that turned orange this time?
Try a few examples of your own and try to predict what will happen in each case.