SOLUTION: If n and p are integers greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p? The answer is 7, but I do not understand how they got this answer. C

Question 466930: If n and p are integers greater than 1 and if p is a factor of both n+3 and n+10, what is the value of p?
The answer is 7, but I do not understand how they got this answer.
Can you help?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
p a factor of n + 3 ==> n + 3 = rp, for some positive integer r
p a factor of n + 10 ==> n + 10 = sp, for some positive integer s
(n + 10 > n+ 3 ==> s > r.)
Hence (n+10) - (n+3) = sp - rp = (s-r)p, or (s-r)p = 7. (Note that s-r is a positive integer.)
Hence p divides the prime number 7 (divisors are 1 and 7.)
This means p = 7, since p > 1.
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