Question

Consider the extremely large integers

x=2*3*5*7*11*13*17*19*23*29 y=29*31*37*41*43*47*53*59*61*67

What is the greatest common divisor of x and y?

Answer 1

It's been a while since I've done something like this, but I believe it would just be 29*67? Since 29 would divide into x and 67 would divide into y? 

Answer 2

Well, the first long expression is the prime factorization of x. The second long expression is the prime factorization of y. The only number that they have in common is 29. If you divide y by 67, you need to also be able to divide x by 67, which you cannot. So 29 is the greatest common divisor of x and y.