Final answer:
To find the GCF of 32x² and 24x²y, the largest common factors, 2³ (or 8) and x², are identified and multiplied, resulting in the GCF of 8x².
Step-by-step explanation:
The question asks to find the Greatest Common Factor (GCF) of two monomials: 32x² and 24x²y. To find the GCF, we will factor out the common terms from both monomials.
First, we factor each monomial individually:
- 32x² = 2µ × x²
- 24x²y = 2³ × 3 × x² × y
We see that both monomials have 2 raised to some power and x² in common. The largest power of 2 that is in both factorizations is 2³ (or 8), since this is the lower of the two powers (5 in the first term and 3 in the second term).
The common term for x² is already at its highest power since it's the same in both monomials. Therefore:
The GCF of 32x² and 24x²y is: 8x².