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    sunnieone's Avatar
    sunnieone Posts: 1, Reputation: 1
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    #1

    Feb 4, 2009, 09:38 AM
    Factors and age
    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:
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    Feb 4, 2009, 10:03 AM

    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
    You can narrow down your search by assuming that the grandather is at least 40 years old, and less than 120.
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