Questions: Find the greatest common factor of the given monomials. 15 x^8 and 12 x The GCF is .

Solution Steps

To find the greatest common factor (GCF) of the given monomials \(15x^8\) and \(12x\), we need to:

1. Find the GCF of the coefficients (15 and 12).
2. Find the GCF of the variable parts (\(x^8\) and \(x\)).

To find the greatest common factor (GCF) of the coefficients 15 and 12, we use the Euclidean algorithm: \[ \text{GCF}(15, 12) = 3 \]

For the variable parts \(x^8\) and \(x\), we take the minimum exponent: \[ \text{GCF}(x^8, x) = x^{\min(8, 1)} = x^1 = x \]

Combining the GCF of the coefficients and the GCF of the variable parts, we get: \[ \text{GCF}(15x^8, 12x) = 3x \]

Final Answer