What is the smallest number with exactly 14 divisors?
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
e.g.
234 ....... 234 234
973 ...... 973 973
Both 6-digit numbers are divisible by 91.
Is this a coincidence?
Are there other patterns and connections?