Which of the following is/are prime numbers?

(A) 241

(B) 337

(C) 391

(D) 571

Choose the correct answer from the options given below:

A prime number is a number greater than 1 that can only be divided by 1 and itself.

To check if a number is prime, test divisibility by prime numbers up to its square root.

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For 241:

$\sqrt{241} \approx 15.5$

Testing primes up to 15: {2, 3, 5, 7, 11, 13}

241 is odd, so not divisible by 2

Digit sum: $2 + 4 + 1 = 7$, not divisible by 3

Doesn't end in 0 or 5, so not divisible by 5

$241 \div 7 = 34.43...$

$241 \div 11 = 21.9...$

$241 \div 13 = 18.5...$

241 is prime.

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For 337:

$\sqrt{337} \approx 18.4$

Testing primes up to 18: {2, 3, 5, 7, 11, 13, 17}

337 is odd

Digit sum: $3 + 3 + 7 = 13$, not divisible by 3

Not divisible by 5

$337 \div 7 = 48.14...$

$337 \div 11 = 30.6...$

$337 \div 13 = 25.9...$

$337 \div 17 = 19.8...$

337 is prime.

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For 391:

$\sqrt{391} \approx 19.8$

Testing primes up to 19: {2, 3, 5, 7, 11, 13, 17, 19}

391 is odd

Digit sum: $3 + 9 + 1 = 13$, not divisible by 3

Not divisible by 5

$391 \div 7 = 55.86...$

$391 \div 11 = 35.5...$

$391 \div 13 = 30.08...$

$391 \div 17 = 23$

$391 = 17 \times 23$

391 is not prime.

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For 571:

$\sqrt{571} \approx 23.9$

Testing primes up to 23: {2, 3, 5, 7, 11, 13, 17, 19, 23}

571 is odd

Digit sum: $5 + 7 + 1 = 13$, not divisible by 3

Not divisible by 5

$571 \div 7 = 81.57...$

$571 \div 11 = 51.9...$

$571 \div 13 = 43.9...$

$571 \div 17 = 33.6...$

$571 \div 19 = 30.05...$

$571 \div 23 = 24.8...$

571 is prime.

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The prime numbers are 241, 337, and 571.

Therefore, options (A), (B), and (D) are prime numbers.