Dropout

Since $gcd(m,n)=2013$ , we can say that $m=2013a$ and $n=2013b$ , where $a$ and $b$ are coprime integers.

Thus, $gcd(\frac {m}{11} , \frac {n}{11}) = gcd(\frac {2013a}{11} , \frac {2013b}{11}) = gcd(183a, 183b)$

Since, $a$ and $b$ are coprime integers, $gcd(\frac {m}{11} , \frac {n}{11}) = gcd(183a, 183b)=183$

As, $gcd(m,n)=x$ and $gcd(\frac{m}{a},\frac{n}{a})=\frac{x}{a}$ Hence for this question, $gcd(\frac{m}{11},\frac{n}{11})=\frac{2013}{11}$ $\Rightarrow gcd(\frac{m}{11},\frac{n}{11})=183$

I just divided 2013 by 11 which yields to 183. :D

we konw that gcd (m, n) = 2013

then

value of gcd (m/11, n/11) = 2013/11

value of gcd (m/11, n/11) = 183 that is answer.

If $m$ and $n$ are divided by an integer $n$ , we can clearly see and say that their g.c.d is also divided by $n$ .

Given that, $\gcd{(m,n)}=2013$

$\implies gcd{(\frac{m}{11}, \frac{n}{11})}=\frac{2013}{11}=\boxed{183}$

gcd of m and n is 2013.. factors of 2013 are 3 11 61. lets consider m and n as 61x11=671 and 3x11=33 note we assumed this nos. by considering the soln we want..there can be other set of nos whose gcd came to be 2013.. thus gcd of 61 and 3 is 183..our final answer..

compare

(m/1,n/1)=2013, while (m/11,n/11) = ?

take a look carefully,

(m/11,n/11)=? are actually 11X smaller than (m/1,n/1)=2013

so,2013 divide by 11 and you will get 183 for (m/11,n/11)

GCD (m, n) = 2013, so m and n can be written in the form 2013(p) and 2013(q), where p and q are numbers less then 2013. Therefore GCD (m/11 , n/11) = GCD (2013/11 p , 2013/11 * q) which is 183 p or 183*q. Since p and q are not coprime the GCD of the two numbers will be 183.

assume gcd(M,N)=Y

form if "M" Exact Division by "X" and "N" Exact Division by "X" then "Y" must Exact Division by "X"

then $gcd(\frac{m}{11},\frac{n}{11})=\frac{2013}{11}=183$

the equation is saying that gcd(m)= 2013 and gcd(n)=2013 then for gcd(m/11) = 2013/11 =183 and also for gcd(n/11) = 183. and the required answer is 183