Identify the greatest common factor of \( 12 x^{2} \) and \( 10 b^{3} x^{4} \)
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To find the greatest common factor (GCF) of \( 12x^{2} \) and \( 10b^{3}x^{4} \), we first analyze the coefficients and the variables separately. The coefficients are 12 and 10, and the GCF of 12 and 10 is 2. Next, we look at the variable parts. The expression \( x^{2} \) indicates we have \( x \) raised to the power of 2 in the first factor, and \( x^{4} \) in the second. The GCF takes the variable with the lowest exponent, which is \( x^{2} \). Since the variable \( b \) doesn’t appear in both expressions, it is not included in the GCF. Thus, combining the GCF of the coefficients and the variable, we get: \[ \text{GCF} = 2x^{2} \]
