Question

If \( 140 = 2^x \times 5^y \times 7^z \), then the value of \( x + y - z \) is:

• A. \( 2 \)
• B. \( 4 \)
• C. \( 3 \)
• D. \( 1 \)

Hint:

To find the exponent values in prime factorization, express the number as a product of prime numbers.

Answer 1

The Correct Option is A

Prime factorizing 140: \[ 140 = 2^2 \times 5^1 \times 7^1. \] Thus: \[ x = 2, \quad y = 1, \quad z = 1. \]4 \[ x + y - z = 2 + 1 - 1 = 2. \]