Question

What is the GCF of 54x5, 80x3, and 24?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the greatest common factor (GCF) of 54x^5, 80x^3, and 24, we need to determine the largest factor that is common to all three terms.

Let's break down each term into its prime factors:

54x^5 = 2 * 3^3 * x^5
80x^3 = 2^4 * 5 * x^3
24 = 2^3 * 3

Now, let's compare the prime factors of each term:

- For the factor of 2: 2^3 is the highest power that appears in all three terms.
- For the factor of 3: 3 appears in both 54x^5 and 24, but 3 does not appear in 80x^3.
- For the factor of x: x^3 is the highest power that appears in both 54x^5 and 80x^3.

Now, let's multiply the common factors together to find the GCF:

GCF = 2^3 * 3 * x^3 = 8 * 3 * x^3 = 24x^3

Therefore, the greatest common factor of 54x^5, 80x^3, and 24 is 24x^3.