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?

Question

please explain how you get the answer

Answer 1

p is a factor of both n+3 and n+10 implies pa = n+3 and pb = n+10 for integers a and b.  Therefore, pb - pa = n + 10 - (n + 3) or p(b - a) = 7.  Since 7 is prime, this implies that either p =1 and b - a = 7 or p  = 7 and b - a = 1.  The first possibility cannot be the case since the problem states that both n and p are integers greater than 1.  Therefore, p must be 7.

Answer 2

substitute n by 2, 3, 4, 5, etc.

you can see that when n = 4, n+3 = 7, n+10 = 14

p is divisible by n+3 and n+10, hence p = 7

Answer 3

these confuse the c**p out of me...

i wish i could help... srry.