Kaplan Nursing Entrance Practice Exam

What is the sum of the prime factors of 144?

1. 10

2. 12

3. 14

4. 16

The correct answer is: 14

To determine the sum of the prime factors of 144, we first need to identify its prime factorization. The prime factorization of 144 is as follows: 1. Begin by dividing 144 by the smallest prime number, 2. \( 144 ÷ 2 = 72 \) 2. Continue dividing by 2: \( 72 ÷ 2 = 36 \) \( 36 ÷ 2 = 18 \) \( 18 ÷ 2 = 9 \) 3. Now, since 9 is no longer divisible by 2, we move to the next prime number, which is 3: \( 9 ÷ 3 = 3 \) \( 3 ÷ 3 = 1 \) Now, we can express 144 as the product of its prime factors: \[ 144 = 2^4 \times 3^2 \] The distinct prime factors here are 2 and 3. To find the sum of these prime factors, we simply add them together: \[ 2 + 3 = 5 \] If we consider that for the purpose of determining unique prime factors, we would actually