Find the common factors of the given terms in each $$ 12 x^{2} y, 18 x y^{2} $$

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To find the **common factors** of the given terms $$ 12x^{2}y $$ and $$ 18xy^{2} $$, we'll follow these steps:

### Step 1: Factor Each Term
First, factor both coefficients and variables:

1. **Factor the Coefficients:**
   - $$ 12 = 2^2 \times 3 $$
   - $$ 18 = 2 \times 3^2 $$

2. **Factor the Variables:**
   - $$ 12x^{2}y = 2^2 \times 3 \times x^2 \times y $$
   - $$ 18xy^{2} = 2 \times 3^2 \times x \times y^2 $$

### Step 2: Identify Common Factors
For each prime factor and variable, take the minimum exponent present in both factorizations:

1. **Numerical Factors:**
   - **2:** Minimum exponent is $$ 2^1 = 2 $$
   - **3:** Minimum exponent is $$ 3^1 = 3 $$

2. **Variable Factors:**
   - **$$ x $$:** Minimum exponent is $$ x^1 $$
   - **$$ y $$:** Minimum exponent is $$ y^1 $$

### Step 3: Multiply the Common Factors
Combine the common factors identified:
$$
\text{GCF} = 2 \times 3 \times x \times y = 6xy
$$

### Conclusion
The **greatest common factor (GCF)** of $$ 12x^{2}y $$ and $$ 18xy^{2} $$ is:
$$
\boxed{6xy}
$$
The greatest common factor of $$ 12x^{2}y $$ and $$ 18xy^{2} $$ is $$ 6xy $$.

Find the common factors of the given terms in each \( 12 x^{2} y, 18 x y^{2} \)

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