Consider the extremely large integers $$x = 2/cdot 3/cdot 5/cdot 7/cdot 11/cdot 13/cdot 17/cdot 19/cdot 23/cdot 29$$ and $$y = 29/cdot 31/cdot 37/cdot 41/cdot 43/cdot 47/cdot 53/cdot 59/cdot 61/cdot 67.$$ What is the greatest common divisor of $x$ and $y$?

Hence, greatest common divisor of x and y is : 29.

Step-by-step explanation:

We are given:

We are given the large integers 'x' and 'y' as:

x=2*3*5*7*11*13*17*19*23*29

We could clearly see that x is the multiplication of all the prime numbers starting from 2 and ending at 29.

we are given y as:

y=29*31*37*41*43*47*53*59*61*67

Clearly we could see that y is also a multiplication of all the prime numbers starting from 29 and ending at 67.

" In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers "

Hence from the expression of x and y we could clearly see that the only common divisor that divides both x and y is 29.

Hence, greatest common divisor of x and y is 29.