$$ imes $$ Find the greatest common factor of the expressions $$ 18 x^{3} y^{3} $$ $$ 12 x^{5} y^{2} $$ $$ 6 x^{2} y^{3} $$

Question

$$ 	imes $$ Find the greatest common factor of the expressions $$ 18 x^{3} y^{3} $$ $$ 12 x^{5} y^{2} $$ $$ 6 x^{2} y^{3} $$

UpStudy AI · Accepted Answer

To find the greatest common factor (GCF) of the expressions:

1. $$ 18x^{3}y^{3} $$
2. $$ 12x^{5}y^{2} $$
3. $$ 6x^{2}y^{3} $$

**Step 1: Find the GCF of the Coefficients**

- The coefficients are 18, 12, and 6.
- The GCF of 18, 12, and 6 is **6**.

**Step 2: Find the GCF of the Variable $$ x $$**

- The exponents of $$ x $$ are 3, 5, and 2.
- The smallest exponent is **2**.
- So, the GCF for $$ x $$ is $$ x^{2} $$.

**Step 3: Find the GCF of the Variable $$ y $$**

- The exponents of $$ y $$ are 3, 2, and 3.
- The smallest exponent is **2**.
- So, the GCF for $$ y $$ is $$ y^{2} $$.

**Combine the GCFs:**

- Multiply the GCFs of the coefficients and the variables:
$$ \text{GCF} = 6 \times x^{2} \times y^{2} = 6x^{2}y^{2} $$

**Final Answer:**
$$ \boxed{6x^{2}y^{2}} $$
The greatest common factor is $$ 6x^{2}y^{2} $$.

\( \times \) Find the greatest common factor of the expressions \( 18 x^{3} y^{3} \) \( 12 x^{5} y^{2} \) \( 6 x^{2} y^{3} \)