Question 8 of 12, step 1 of 1 Find the GCF (greatest common factor) of the following terms. $$ \left\{55 x y^{2}, 20\right\} $$

Question

UpStudy AI · Accepted Answer

To find the greatest common factor (GCF) of the terms $$ 55xy^2 $$ and $$ 20 $$, we will follow these steps:

1. **Factor each term into its prime factors.**
2. **Identify the common factors.**
3. **Multiply the common factors to find the GCF.**

### Step 1: Factor each term

- For $$ 55xy^2 $$:
  - The prime factorization of $$ 55 $$ is $$ 5 \times 11 $$.
  - Therefore, $$ 55xy^2 = 5 \times 11 \times x \times y^2 $$.

- For $$ 20 $$:
  - The prime factorization of $$ 20 $$ is $$ 2^2 \times 5 $$.
  - Therefore, $$ 20 = 2^2 \times 5 $$.

### Step 2: Identify the common factors

Now we list the factors:
- Factors of $$ 55xy^2 $$: $$ 5, 11, x, y, y $$
- Factors of $$ 20 $$: $$ 2, 2, 5 $$

The only common factor between $$ 55xy^2 $$ and $$ 20 $$ is $$ 5 $$.

### Step 3: Multiply the common factors

Since the only common factor is $$ 5 $$, the GCF is:

$$
\text{GCF} = 5
$$

Thus, the greatest common factor of $$ 55xy^2 $$ and $$ 20 $$ is $$ 5 $$.
The greatest common factor (GCF) of $$ 55xy^2 $$ and $$ 20 $$ is $$ 5 $$.

Question 8 of 12, step 1 of 1 Find the GCF (greatest common factor) of the following terms. \[ \left\{55 x y^{2}, 20\right\} \]