Question

x equals 3 to the power of 4 times 5 cubed times 7 times 11 to the power of 4 y equals 3 squared times 5 to the power of 4 times 7 times 13 to the power of 4 What is the prime factorization for gcd(x, y).

Answer 1

Answer:

$gcd(x, y) = 3^2\times 5^3\times 7$                  

Step-by-step explanation:

We are given the following in the question:

$x = 3^4\times 5^3\times 7\times 11^4\\y = 3^2\times 5^4\times 7\times 13^4$

We have to find prime factorization for gcd(x, y).

To find the greatest common factor for x and y ,we find the common factors in the prime factorization of x and y.

The common factors are:

$g.c.d(x,y) = 3^2\times 5^3\times 7 = 7875$

The prime factorization for gcd(x,y) is

$7875\\= 3\times 3\times 5\times 5\times 5\times 7\\ = 3^2\times 5^3\times 7$