Question:

Which of the following is not a prime number?

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For prime check, only test divisibility by prime numbers up to the square root of the given number. This saves time in exams.
Updated On: Aug 12, 2025
  • 23
  • 29
  • 43
  • 21
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The Correct Option is D

Solution and Explanation

Step 1: Definition — A prime number is a number greater than 1 which has only two factors: 1 and itself.
Step 2: Check each option one-by-one: - 23: Divisibility test — not divisible by 2, 3, 5, or 7 (primes ≤ √23), hence prime.
- 29: Divisibility test — not divisible by 2, 3, or 5 (primes ≤ √29), hence prime.
- 43: Divisibility test — not divisible by 2, 3, 5, or 7 (primes ≤ √43), hence prime.
- 21: Divisibility test — divisible by 3 (21 ÷ 3 = 7), hence composite.
Step 3: Since 21 has more than two factors (1, 3, 7, 21), it is not prime.
Step 4: Elimination reasoning: - Option (a) 23 — prime, so not correct.
- Option (b) 29 — prime, so not correct.
- Option (c) 43 — prime, so not correct.
- Option (d) 21 — composite, correct answer.
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