Is there an efficient way to work out how many factors a large number has?
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.
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?... View the problem
This problem offers a twist on the usual way of thinking about divisibility tests - rather than checking to see if a number is divisible by 2, 3, 4 or 6, students are asked to construct numbers that meet the necessary criteria.
American Billions is an engaging extension activity which uses similar ideas to the ones met in this problem.
The interactivity in the problem Largest Even offers students practice in finding even numbers using just two digits. In a similar way, the rest of the challenges in this problem could be adapted to two-digit numbers.