Find the GCF of 96x5 and 64x2

Find the GCF of 96×5 and 64×2

The Correct Answer and Explanation is:

✅ Greatest Common Factor (GCF) of 96x⁵ and 64x²:

Answer:
The GCF of 96x⁵ and 64x² is 32x².

Explanation:

To find the Greatest Common Factor (GCF) of two algebraic expressions, we must find the largest expression that divides both terms exactly—this includes both their numerical coefficients and their variable parts.

Let’s break it down step by step.

1. Find the GCF of the numerical coefficients:

The two coefficients are:

We factor each number:

96 = 2⁵ × 3
64 = 2⁶

The common factor is the lowest power of the common prime factor, which is 2:

GCF(96, 64) = 2⁵ = 32

2. Find the GCF of the variable parts:

We have:

x⁵
x²

When variables are raised to powers, the GCF is the variable raised to the smallest exponent:

GCF(x⁵, x²) = x²

3. Combine the two GCFs:

Now combine the GCF of the numerical coefficients (32) and the variable part (x²):

GCF(96x⁵, 64x²) = 32x²

🔁 Verification:

Let’s divide both expressions by 32x²:

96x⁵ ÷ 32x² = 3x³
64x² ÷ 32x² = 2

Both divisions give whole expressions, confirming that 32x² is indeed a common factor.

Also, it is the greatest common factor because no larger number or variable expression can divide both 96x⁵ and 64x² without leaving a remainder.