Question

Find the greatest common factor of 16x^4y^{3 } 24x^3 y^4

Answer 1

The greatest common factor of 16x^4y^3 and 24x^3y^4 is determined by finding the common numerical factors and the highest powers of variables present in both terms. The GCF is 8x^3y^3.

Step-by-step explanation:

To find the greatest common factor (GCF) of the terms 16x^4y^3 and 24x^3y^4, we need to factor both numerical coefficients and variables separately and then determine the common factors.

First, let's factor the numerical coefficients:

• 16 = 2^4
• 24 = 2^3 × 3

The common factors of the numerical coefficients are 2^3 since that's the highest power of 2 that is contained in both.

Now let's look at the variables:

• x terms: x^4 and x^3 have a common factor of x^3.
• y terms: y^3 and y^4 have a common factor of y^3.

Combining the common numerical and variable factors, the GCF is 2^3x^3y^3, which simplifies to 8x^3y^3.