<p>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.</p>
<p>a). 3
b). 7
c). 10
d). 13
e). 30</p>
<p>P must be 7 and n must be 11. When n is 11, n+3 becomes 14 and 7 is a factor of 14. When n is 11, n+10 is 21 and 7 is a factor of 21 and so the value of P must be 7 for that to be true. I don’t know I just did guess and check using the answers given.</p>
<p>is there any way to systematically solve it?</p>
<p>If p is a factor of both (n+3) and (n+10) then the difference of (n+3) and (n+10) must also be a factor of p.</p>
<p>i.e., p must be a factor of 7.</p>
<p>Therefore, p is either 1 or 7.</p>