express the prime factorization 2 remainder 3 . 5 remainder 2 . 11 as a whole number

Answer 1

To express the prime factorization \(2 , \text{remainder} , 3 \cdot 5 , \text{remainder} , 2 \cdot 11\) as a whole number, we first need to interpret what "remainder" means in this context. It appears that each prime factor is followed by a "remainder" that indicates the exponent in its prime factorization.

Here, the expression seems to mean:

• \(2\) with a remainder of \(3\), which can be interpreted as \(2^3\)
• \(5\) with a remainder of \(2\), which can be interpreted as \(5^2\)
• and \(11\) with no remainder specified, which is \(11^1\) or simply \(11\)

Thus, we can rewrite the expression as:

\[ 2^3 \cdot 5^2 \cdot 11^1 \]

Now, we can calculate the whole number:

1. Calculate \(2^3\): \[ 2^3 = 8 \]

2. Calculate \(5^2\): \[ 5^2 = 25 \]

3. Combine them: \[ 8 \cdot 25 = 200 \]

4. Now multiply by \(11\): \[ 200 \cdot 11 = 2200 \]

Thus, the whole number is \(2200\).