Question

If \( 156 = 2^x \times 3^y \times 13^z \), then \( x + y + z = ? \)

• A. 4
• B. 5
• C. 3
• D. 6

Hint:

To find the prime factorization of a number, start dividing it by the smallest prime numbers until all factors are prime.

Answer 1

The Correct Option is A

Step 1: Prime factorization of 156: \[ 156 = 2^2 \times 3 \times 13 \] Step 2: Comparing this with the expression \( 156 = 2^x \times 3^y \times 13^z \), we get: \[ x = 2, \quad y = 1, \quad z = 1 \] Thus, \( x + y + z = 2 + 1 + 1 = 4 \).