1. **State the problem:** Find the greatest common factor (GCF) of the terms $63x^2y$, $9x^3y^4$, and $90x^3y$. 2. **Recall the formula and rules:** The GCF is found by taking the lowest powers of all common prime factors and variables present in each term. 3. **Factor each term into primes and variables:** - $63x^2y = 7 \times 3^2 \times x^2 \times y$ - $9x^3y^4 = 3^2 \times x^3 \times y^4$ - $90x^3y = 2 \times 3^2 \times 5 \times x^3 \times y$ 4. **Find the common prime factors with lowest powers:** - For numbers: common prime factors are $3^2$ (since all have at least $3^2$) - For variables $x$: lowest power is $x^2$ - For variables $y$: lowest power is $y^1$ 5. **Write the GCF:** $$\text{GCF} = 3^2 \times x^2 \times y = 9x^2y$$ 6. **Final answer:** The greatest common factor of the list is $9x^2y$.