Joans age was a factor of her grandfathers age for 6 consecutive years. What were her grandfathers ages during this time?

I don't even know how to get started on this one. Any help would be greatly appreciated. :eek:

For Joan's age to be a factor of the grandfather's age, her grandfather's age can't be a prime number in any of the 6 years, EXCEPT for possibly the first if Joan is 1 year old that year. So you are looking for either:

1. A prime followed by 5 consecutive non-primes (in which case Joan is 1 that first year), where the non-primes are in turn divisible by 2, 3, 4, 5 and 6, or

2. A sequence of 6 consecutive primes that are in turn divisible by a sequence of 6 consecutive numbers.

It would help to start with a list of primes - see:
List of prime numbers - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/List_of_prime_numbers)
You can narrow down your search by assuming that the grandather is at least 40 years old, and less than 120.