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Which of the following is a prime number?
437
373
161
221
373
To test if a number is prime, check divisibility by prime numbers up to its square root. For 373, 373≈19.3, and it is not divisible by 2,3,5,7,11,13,17,19.
Four numbers are given in the options: 437, 373, 161, and 221.
Prime Number Check: Test divisibility by all primes p≤n
To test if a number is prime, check divisibility by prime numbers up to its square root. For 373, 373≈19.3, and it is not divisible by 2,3,5,7,11,13,17,19.
Confusing prime numbers with composite numbers like 437 (19×23), 161 (7×23), or 221 (13×17).
Step 1: Analyze Option A (437)
Check if 437 is divisible by small prime numbers. We find that 437=19×23. Hence, 437 is a composite number.
437=19×23
Step 2: Analyze Option B (373)
Test divisibility of 373. 373≈19.3. Primes to test are 2,3,5,7,11,13,17,19. None of these divide 373. Therefore, 373 is a prime number.
373 is prime
Step 3: Analyze Option C (161)
Check factors of 161. We find that 161=7×23. Hence, 161 is a composite number.
161=7×23
Step 4: Analyze Option D (221)
Check factors of 221. We find that 221=13×17. Hence, 221 is a composite number.
221=13×17
B is correct because 373 has no positive divisors other than 1 and itself, making it a prime number, whereas 437, 161, and 221 are composite numbers.
Always remember common factorizations like 13×17=221 and 19×23=437 which frequently appear in aptitude exams.
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