Which of the following numbers are prime? 1, 6.3, 11, 14, 13, 21, 23, 4/5,…

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Which of the following numbers are prime? 1, 6.3, 11, 14, 13, 21, 23, 4/5, 100, 123.

  1. A.

    11, 13, 23

  2. B.

    22, 21, 14

  3. C.

    16, 17, 18

  4. D.

    31, 56, 96

Attempted by 1 students.

Show answer & explanation

Correct answer: A

A prime number is a whole number greater than 1 with exactly two factors: 1 and itself. A composite number has more than two factors. A number that is not a whole number — a decimal or a fraction — cannot be prime or composite at all.

Number

Classification

Reason

1

Not prime

Not greater than 1

6.3

Not prime

Decimal — not a whole number

11

Prime

Divisible only by 1 and itself

14

Not prime

14 = 2 × 7

13

Prime

Divisible only by 1 and itself

21

Not prime

21 = 3 × 7

23

Prime

Divisible only by 1 and itself

4/5

Not prime

Fraction — not a whole number

100

Not prime

100 = 2 × 2 × 5 × 5 (many factors)

123

Not prime

123 = 3 × 41

Checking each candidate prime by trial division up to its square root confirms this: 11 (√11 ≈ 3.3) is not divisible by 2 or 3; 13 (√13 ≈ 3.6) is not divisible by 2 or 3; 23 (√23 ≈ 4.8) is not divisible by 2 or 3. No smaller divisor exists for any of them, so all three are genuinely prime.

So the primes in the list are exactly 11, 13, and 23 — the only three numbers in the list with exactly two factors.

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