Question

What is the exponent of \(2\) in the prime factorization of \(192\)?

• A. \(2\)
• B. \(3\)
• C. \(6\)
• D. \(5\)

Hint:

Break numbers into convenient powers: \(192=64\times3=2^6\times3\). Spotting perfect powers speeds up prime factorization.

Answer 1

The Correct Option is C

Step 1: Factorize \(192\).
\(192 = 64 \times 3 = 2^6 \times 3.\)
Step 2: Read off the exponent of \(2\).
In \(192 = 2^6 \times 3\), the exponent of \(2\) is \(6\).
Step 3: Conclude.
Therefore, the required exponent is \(6\).