Question

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

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

To find the sum of powers of prime factors, first perform the prime factorization and then sum the exponents.

Answer 1

The Correct Option is B

Step 1: Prime factorization of 144.
First, factorize 144: \[ 144 \div 2 = 72 \quad \Rightarrow \quad 72 \div 2 = 36 \quad \Rightarrow \quad 36 \div 2 = 18 \quad \Rightarrow \quad 18 \div 2 = 9 \] \[ 9 \div 3 = 3 \quad \Rightarrow \quad 3 \div 3 = 1 \] So, 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.
Therefore, the sum of powers of prime factors of 144 is $6$.