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

`gcd(x, y) = 3^2* 5^3* 7`

Explanation:

We are given the following in the question:

`x = 3^4* 5^3* 7* 11^4\\y = 3^2* 5^4* 7* 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* 5^3* 7 = 7875`

The prime factorization for gcd(x,y) is

`7875\\= 3* 3* 5* 5* 5* 7\\ = 3^2* 5^3* 7`