Question

The sum of powers of prime factors of the number 144 will be:

• A. 5
• B. 4
• C. 6
• D. 3

Hint:

To find the sum of powers of prime factors, first express the number as a product of prime factors, then add the exponents.

Answer 1

The Correct Option is B

Step 1: Find the prime factorization of 144.
We start by finding the prime factorization of 144: \[ 144 \div 2 = 72 \quad \text{(Divide by 2)} \] \[ 72 \div 2 = 36 \quad \text{(Divide by 2)} \] \[ 36 \div 2 = 18 \quad \text{(Divide by 2)} \] \[ 18 \div 2 = 9 \quad \text{(Divide by 2)} \] \[ 9 \div 3 = 3 \quad \text{(Divide by 3)} \] \[ 3 \div 3 = 1 \quad \text{(Divide by 3)} \] Thus, the prime factorization of 144 is: \[ 144 = 2^4 \times 3^2 \]
Step 2: Find the sum of the powers of the prime factors.
The powers of the prime factors are \( 4 \) for \( 2 \) and \( 2 \) for \( 3 \). The sum of these powers is: \[ 4 + 2 = 6 \]
Step 3: Conclusion.
Thus, the sum of the powers of the prime factors of 144 is 6. Therefore, the correct answer is (C) 6.