What is the GCF of 54x^5, 80x^3, and 24?
To find the greatest common factor (GCF) of 54x^5, 80x^3, and 24, we need to factor each term completely.
First, we can factor out any common factors from each term:
54x^5 = 2 * 3^3 * x^5
80x^3 = 2^4 * 5 * x^3
24 = 2^3 * 3
Now, we need to find the highest power of each prime factor that appears in all three terms. The GCF will be the product of these highest powers.
Prime factor 2 appears with the highest power in 54x^5 and 80x^3, so its highest power is 4.
Prime factor 3 appears with the highest power in 54x^5 and 24, so its highest power is 3.
Prime factor 5 appears with the highest power only in 80x^3.
Therefore, the GCF of 54x^5, 80x^3, and 24 is 2^3 * 3^3 * 5 = 2160.