Question

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 $y$?

Answer 1

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

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.