Which statement about the Sieve of Eratosthenes is true?

• A. It marks multiples of each prime to identify primes up to a given limit.
• B. It tests divisibility only by 2.
• C. It requires recursion to work.
• D. It sorts primes after generation.

Answer: (A)

The Sieve of Eratosthenes works by marking multiples of each found prime to identify primes up to a given limit. You start with 2, mark all its multiples as composite, then move to the next number that hasn’t been marked and repeat. The numbers left unmarked after processing up to the limit are the primes. This single idea—eliminating composites by crossing off multiples of known primes—embodies the method.

The other statements don’t fit because marking only multiples of 2 would miss many composites; the process does not rely on recursion; and there isn’t a separate step that “sorts” primes after generation—the primes are identified by elimination, not by ordering.