Reduce the fraction 2714/5074 to lowest terms.

Introduction / Context:
This question checks whether you can simplify a relatively large fraction to its lowest terms. Reducing fractions is often needed in data interpretation, ratio problems and simplifying algebraic expressions.

Given Data / Assumptions:

• Fraction: 2714/5074.
• We need to express this fraction in lowest terms.
• We assume both numerator and denominator are positive integers.

Concept / Approach:
To reduce a fraction to lowest terms, we divide both numerator and denominator by their greatest common divisor. The main task is to find that greatest common divisor, often by systematic trial with prime factors or by the Euclidean algorithm.

Step-by-Step Solution:

Verification / Alternative check:
You can also verify by direct division: 2714 ÷ 23 = 118 and 5074 ÷ 43 = 118, so both numerator and denominator share the factor 118. Dividing by 118 yields 23/43 directly.

Why Other Options Are Wrong:
17/23, 29/43 and 31/37 do not equal 2714/5074 when cross multiplied. For example, comparing 2714/5074 with 23/43 works, but cross multiplying with 17/23 gives mismatched products, so those fractions are not equivalent.

Common Pitfalls:
Many candidates stop after dividing by 2 and incorrectly assume that 1357/2537 is already in lowest terms. Others may guess simplifications instead of systematically checking for common factors. Using a structured factorization or Euclidean algorithm is more reliable.

Final Answer:
The fraction 2714/5074 in lowest terms is 23/43.