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.
Will each method always work?
Where is the $20 \times 20$? Where is the $20 \times 3$? ...
Offer students this worksheet with the methods for $23 \times 21$ to make sense of first, as there are no 'carry' digits so it is clearer to see what is going on.
Stu Cork created this GeoGebra file to use with this problem, which he has kindly given us permission to share.