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.
Think of any three-digit number.
Repeat the digits
234 ....... 234 234
973 ...... 973 973
Both 6-digit numbers are divisible by 91.
Is this a coincidence?
Are there other patterns and connections?