Calculator overflow

You can quickly take note that gcd(110,20)=10. With this you can substitute $2^{10}=x$ . Doing this gives the values of $gcd(x^{11}-1,x^2-1)$ . Factoring both expressions we find: $x^{11}-1=(x^{10}+x^9+...+x+1)(x-1) \\ x^2-1=(x+1)(x-1)$ Notice that both expressions share a factor of $x-1=2^{10}-1=1023$