Compute $gcd\left(1714, 1814\right)$ using Euclidean Algorithm So I know the answer for this is $2$, but based on my own work, I can't get to that solution. I haven't done a gcd before where $b>a$. I thought I could just flip the numbers and use the same method but that didn't seem to work. Here's what I have so far, what I am doing wrong? 
$$\begin{align}
    \mathrm{gcd}(1714, 1814) &= \mathrm{gcd}(1814, 1714) \\
    \mathrm{gcd}(1814, 1714) &= (1714, 100)\\
                    &= (100, 14)\\
                    &= (14, 9)\\
                    &= (9, 5)\\
                    &= (5, 4)\\
                    &= (4, 1)\\
                    &= (1, 0)\\
                    &= 1\\
\end{align}
$$
I basically tried using the Euclidian algorithm method where you keep doing long division into each number to get the remainder and continue with that process. 
 A: The answer is clearly wrong; both $1714$ and $1814$ are even, so $2$ divides both; the gcd is at least $2$.
In your solution, you really should write $\gcd(1814,1714)=\gcd(1714,100)=\cdots$ etc. The remainder when you divide $100$ by $14$ is $2$
($100=7\times 14+2$) so $\gcd(100,14)=\gcd(14,2)$ etc.
A: \begin{align}
GCD(1814,1714)&=(1714,100)\\
&=(100,14)\\
&=(14,2)\\
\end{align}
 So, $2$ is the $GCD$
A: When you reach (100,14) the next step gives (14,2) since $14 \times 7 = 98$ and $100 - 98 = 2$. 
A: written as a continued fraction: 
$$ \frac{ 1814 }{ 1714 } = 1 +  \frac{ 100 }{ 1714 } $$ 
 $$ \frac{ 1714 }{ 100 } = 17 +  \frac{ 14 }{ 100 } $$ 
 $$ \frac{ 100 }{ 14 } = 7 +  \frac{ 2 }{ 14 } $$ 
 $$ \frac{ 14 }{ 2 } = 7 +  \frac{ 0 }{ 2 } $$ 
 Simple continued fraction tableau:
 $$ 
 \begin{array}{cccccccccc}
 & & 1 & & 17 & & 7 & & 7 & \\ 
  \frac{ 0 }{ 1 }   &   \frac{ 1 }{ 0 }   & &   \frac{ 1 }{ 1 }   & &   \frac{ 18 }{ 17 }   & &   \frac{ 127 }{ 120 }   & &   \frac{ 907 }{ 857 }  
 \end{array}
 $$ 
 $$  $$ 
 $$ 
 \begin{array}{ccc}
  \frac{ 1 }{ 0 }   &     \mbox{digit}  &  1  \\  
  \frac{ 1 }{ 1 }   &     \mbox{digit}  &  17  \\  
  \frac{ 18 }{ 17 }   &     \mbox{digit}  &  7  \\  
  \frac{ 127 }{ 120 }   &     \mbox{digit}  &  7  \\  
  \frac{ 907 }{ 857 }   &     \mbox{digit}  &  0  \\  
 \end{array}
 $$ 
$$ 907 \cdot 120 - 857 \cdot 127 = 1 $$ 
$$  \gcd( 1814, 1714 ) = 2  $$
 $$ 1814 \cdot 120 - 1714 \cdot 127 = 2 $$ 
