Question 1173509
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I will help you to solve the second problem.


<pre>
    n is a natural number.  Find the common Greatest Common Divisor (GCD) of numbers (2n+25) and (n+15).
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Solution</U>



<pre>
Let integer number d is the common divisor of (2n+25) and (n+5).


Then it divides the difference 


    (2n+25) - 2*(n+5) = (2n+5) - (2n+10) = 2n + 5 - 2n - 1- = -5.


Thus, any common divisor of the numbers (2n+5) and (n+5) divides the number -5.


It means that the Common Greatest Divisor (GCD) of these numbers is EITHER 5 OR 1.


It can not be any other number.




Example 1:   Let n = 10.

             Then the numbers (2n+5) = 25  and  (n+5) = 15.

             Their Greatest Common Divisor is 5.



Example 2:   Let n = 7.

             Then the numbers (2n+5) = 19  and  (n+5) = 12.

             Their Greatest Common Divisor is 1.



Thus I explained you the solution and illustrated it by examples.


<U>ANSWER</U>.  &nbsp;&nbsp;GCD of these numbers is  &nbsp;EITHER &nbsp;5 &nbsp;OR &nbsp;1.
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The solution is completed.



After learning it from me, &nbsp;now solve the &nbsp;problem #3 &nbsp;ON &nbsp;YOUR &nbsp;OWN.



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