Question

Find the greatest common divisor of the term 144x^2y^2 and 81xy.

A) 9xy
B) 18xy^2
C) 3xy
D) 27x^2y^3

Answer 1

The greatest common divisor of 144x^2y^2 and 81xy is determined by factoring both terms and finding the highest powers of common factors for the numerical coefficients and each variable. The GCD is 9xy, which is option A).

Step-by-step explanation:

To find the greatest common divisor (GCD) of the terms 144x^2y^2 and 81xy, we need to factor each term and then determine the highest powers of common factors they share.

First, factor the numerical coefficients: 144 = 2^4 × 3^2 and 81 = 3^4.

Now factor the variables: x^2y^2 and xy can be written as (x × x)(y × y) and (x)(y), respectively.

The highest powers of common factors for numbers and variables are:

• For the numerical coefficient: the highest power of 3 that divides both 144 and 81 is 3^2, which is 9.
• For x: the lowest power of x in both terms is x.
• For y: the lowest power of y in both terms is y.

Therefore, the GCD of 144x^2y^2 and 81xy is 9xy, which corresponds to option A).