Question

The sum of the exponents of the prime factors in the prime factorization of 156 is

• A. 2
• B. 3
• C. 4
• D. 6

Answer 1

The Correct Option is C

Given number:

156

Goal: Find the sum of the exponents of the prime factors in the prime factorization of 156.

Step 1: Perform the prime factorization of 156.

Start by dividing 156 by the smallest prime number, 2: 

156 ÷ 2 = 78

Now divide 78 by 2 again:

78 ÷ 2 = 39

39 is not divisible by 2, so move to the next prime number, 3:

39 ÷ 3 = 13

13 is a prime number, so the prime factorization of 156 is:

156 = 2² × 3 × 13

Step 2: Find the sum of the exponents of the prime factors.

The exponents in the prime factorization 2² × 3¹ × 13¹ are 2, 1, and 1.

The sum of the exponents is:

2 + 1 + 1 = 4

Answer: The sum of the exponents of the prime factors in the prime factorization of 156 is 4.

Answer 2

To find the sum of the exponents of the prime factors in the prime factorization of 156, follow these steps:
Perform prime factorization on 156:
Divide 156 by 2 (the smallest prime number) which gives 156 ÷ 2 = 78.
Divide 78 by 2, resulting in 78 ÷ 2 = 39.
Now 39 is not divisible by 2. Move to the next prime number, which is 3. Dividing 39 by 3 gives 39 ÷ 3 = 13.
Finally, 13 is a prime number itself and cannot be divided further.
Thus, the prime factorization of 156 is 2² × 3¹ × 13¹.
Add the exponents of the prime factors: 2 (for 2²) + 1 (for 3¹) + 1 (for 13¹) = 4.
Therefore, the sum of the exponents of the prime factors is 4.