Question
22 • 3 • 52 is the prime factorization for which of the following numbers?
(1 point)
Responses
990
990
1,700
1,700
300
300
880
(1 point)
Responses
990
990
1,700
1,700
300
300
880
Answers
GPT-4o mini
To find out which number corresponds to the prime factorization \( 22 \cdot 3 \cdot 52 \), we will first calculate it.
1. **Calculate \( 22 \cdot 3 \)**:
\[
22 \cdot 3 = 66
\]
2. **Next, calculate \( 66 \cdot 52 \)**:
\[
66 \cdot 52 = 3432
\]
Now, let's evaluate the options given:
- **990**: \( 990 = 2 \cdot 3 \cdot 5 \cdot 11 \)
- **1,700**: \( 1,700 = 2^2 \cdot 5^2 \cdot 17 \)
- **300**: \( 300 = 2^2 \cdot 3 \cdot 5^2 \)
- **880**: \( 880 = 2^4 \cdot 5 \cdot 11 \)
None of these match \( 3432 \).
Let's verify whether the prime factorization \( 22 \cdot 3 \cdot 52 \) could represent any of the given options if miscalculated. The individual prime factor breakdown is \( 22 = 2 \cdot 11 \), \( 3 \) is prime, and \( 52 = 2^2 \cdot 13 \).
If we multiply directly:
\[
22 \cdot 3 = 66 = 2 \cdot 3 \cdot 11
\]
\[
52 = 2^2 \cdot 13
\]
So \( 22 \cdot 3 \cdot 52 = (2 \cdot 3 \cdot 11) \cdot (2^2 \cdot 13) = 2^3 \cdot 3 \cdot 11 \cdot 13 \), which computes to a number too large for the options provided.
To validate this, let’s break down each option to check the composite number structure, but as we’ve derived \( 3432 \), this does not land us with an answer directly related to the options.
After checking through both the multiple values as well as examining the process used to expand \( 22 \cdot 3 \cdot 52 \):
- **None** of the given options (990, 1,700, 300, or 880) correlate to \( 22 \cdot 3 \cdot 52 \).
Thus, there seems to be a mismatch in the options available unless misinterpretation of values occurred.
Conclusively, we conferred:
The answer does not directly equate to any of the proposed numbers provided in the question; hence:
- **None of these values represent \( 22 \cdot 3 \cdot 52 \) (3432)**.
1. **Calculate \( 22 \cdot 3 \)**:
\[
22 \cdot 3 = 66
\]
2. **Next, calculate \( 66 \cdot 52 \)**:
\[
66 \cdot 52 = 3432
\]
Now, let's evaluate the options given:
- **990**: \( 990 = 2 \cdot 3 \cdot 5 \cdot 11 \)
- **1,700**: \( 1,700 = 2^2 \cdot 5^2 \cdot 17 \)
- **300**: \( 300 = 2^2 \cdot 3 \cdot 5^2 \)
- **880**: \( 880 = 2^4 \cdot 5 \cdot 11 \)
None of these match \( 3432 \).
Let's verify whether the prime factorization \( 22 \cdot 3 \cdot 52 \) could represent any of the given options if miscalculated. The individual prime factor breakdown is \( 22 = 2 \cdot 11 \), \( 3 \) is prime, and \( 52 = 2^2 \cdot 13 \).
If we multiply directly:
\[
22 \cdot 3 = 66 = 2 \cdot 3 \cdot 11
\]
\[
52 = 2^2 \cdot 13
\]
So \( 22 \cdot 3 \cdot 52 = (2 \cdot 3 \cdot 11) \cdot (2^2 \cdot 13) = 2^3 \cdot 3 \cdot 11 \cdot 13 \), which computes to a number too large for the options provided.
To validate this, let’s break down each option to check the composite number structure, but as we’ve derived \( 3432 \), this does not land us with an answer directly related to the options.
After checking through both the multiple values as well as examining the process used to expand \( 22 \cdot 3 \cdot 52 \):
- **None** of the given options (990, 1,700, 300, or 880) correlate to \( 22 \cdot 3 \cdot 52 \).
Thus, there seems to be a mismatch in the options available unless misinterpretation of values occurred.
Conclusively, we conferred:
The answer does not directly equate to any of the proposed numbers provided in the question; hence:
- **None of these values represent \( 22 \cdot 3 \cdot 52 \) (3432)**.