1. **State the problem:** Find the greatest common factor (GCF) of the monomials $10a^3$, $12a^2$, and $14a$. 2. **Recall the formula and rules:** The GCF of monomials is found by taking the GCF of the coefficients and the lowest power of the common variables. 3. **Find the GCF of the coefficients:** - Coefficients are 10, 12, and 14. - Prime factorization: $$10 = 2 \times 5$$ $$12 = 2^2 \times 3$$ $$14 = 2 \times 7$$ - Common prime factors: only 2. - So, GCF of coefficients is $2$. 4. **Find the GCF of the variable parts:** - Variables are $a^3$, $a^2$, and $a$. - The lowest power of $a$ among them is $a^1 = a$. 5. **Combine the GCF of coefficients and variables:** $$\text{GCF} = 2a$$ **Final answer:** The greatest common factor of $10a^3$, $12a^2$, and $14a$ is $2a$.