Identify the greatest common factor of $$ 12 x^{2} $$ and $$ 10 b^{3} x^{4} $$

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1. Factor the numerical coefficients:
   - The factors of $$12$$ are $$2 	imes 2 	imes 3$$.
   - The factors of $$10$$ are $$2 	imes 5$$.
   - The greatest common factor of $$12$$ and $$10$$ is $$2$$.

2. For the variable part, compare the exponents of $$x$$:
   - In $$12x^{2}$$, the exponent of $$x$$ is $$2$$.
   - In $$10b^{3}x^{4}$$, the exponent of $$x$$ is $$4$$.
   - The smallest exponent is $$2$$, so the common factor involving $$x$$ is $$x^{2}$$.

3. The variable $$b$$ does not appear in the first term, so it is not considered for the greatest common factor.

Thus, the greatest common factor is $$2x^{2}$$.
The greatest common factor is $$2x^{2}$$.

Identify the greatest common factor of \( 12 x^{2} \) and \( 10 b^{3} x^{4} \)

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