Identify the Number from Given Prime Factors: 2, 2, 5, and 11

Let's tackle the problem of finding the number whose prime factors are $2, 5, 11,$ and another $2$.

First, we need to understand what the problem is asking us to find. It describes a number that is completely defined by its prime factors, given by $2, 5, 11,$ and another $2$. Essentially, we are tasked with determining the composite number that results from multiplying these prime factors together.

• Step 1: Identify the given prime factors: $2, 5, 11,$ and another $2$. This means we actually have $2^2 \times 5 \times 11$.
• Step 2: Multiply the factors together to find the original number. We will break down the calculation for clarity:
  • First, calculate $2^2 = 4$.
  • Next, multiply this result by 5: $4 \times 5 = 20$.
  • Finally, multiply the previous result by 11: $20 \times 11 = 220$.

After performing these calculations, we find that the correct number is indeed 220.

Therefore, the solution to the problem is $220$.