Question

The greatest prime factor of 144 is \( x \)
The greatest prime factor of 96 is \( y \)

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

To find the greatest prime factor of a number, first perform prime factorization and identify the largest prime factor.

Answer 1

The Correct Option is C

Step 1: Prime factorization of 144.
The prime factorization of 144 is: \[ 144 = 2^4 \times 3^2 \] The greatest prime factor of 144 is 3. Therefore, \( x = 3 \).
Step 2: Prime factorization of 96.
The prime factorization of 96 is: \[ 96 = 2^5 \times 3 \] The greatest prime factor of 96 is also 3. Therefore, \( y = 3 \).
Step 3: Conclusion.
Since both \( x = 3 \) and \( y = 3 \), the two quantities are equal.
Final Answer: \[ \boxed{\text{The two quantities are equal.}} \]