Question

The sum of the powers of prime factors in prime factorization of 144 is:

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

In prime factorization, sum the exponents of the prime factors to find the total sum of the powers.

Answer 1

The Correct Option is B

The prime factorization of 144 is: \[ 144 = 2^4 \times 3^2 \]
Step 1: Identifying the prime factors.
The prime factors of 144 are 2 and 3.
Step 2: Summing the powers of the prime factors.
The powers of the prime factors are 4 and 2 (for 2 and 3, respectively). The sum of the powers is: \[ 4 + 2 = 6 \]
Step 3: Conclusion.
Therefore, the sum of the powers of prime factors in the prime factorization of 144 is 6. The correct answer is (B).