Q2
1 markMCQSection A

  1. The natural number 2 is : (a) a prime number (b) a composite number (c) prime as well as composite (d) neither prime nor composite

Real Numbers
Prime and composite numbers

Options

(A)a prime number
(B)a composite number
(C)prime as well as composite
(D)neither prime nor composite
Official Answer

(a) a prime number — 2 has exactly two factors, 1 and 2, satisfying the definition of a prime; it is also the only even prime.

prime numbertwo factors1 and itselfonly even primecomposite numbernatural numberfactors of 2

Marking Scheme

  • 11 mark: correct option (a) a prime number.
  • 2Expected reasoning: 2 has exactly two factors, 1 and 2, so it is prime; it is also the only even prime.

Hint

Count the factors of 2 — a number with exactly two factors (1 and itself) is prime.

Quick Oral Answer

2 is a prime number because it has exactly two factors, 1 and 2, and it is special as the only even prime.

Analysis & Explanation

This MCQ tests the definition of a prime number using 2 as the special case.


Concept

  • A prime number has exactly two distinct factors: 1 and itself.
  • 2 has factors 1 and 2 only, so it satisfies this definition.

Key points

  • 2 is the only even prime; every other even number has 2 as an extra factor, making it composite.
  • A number cannot be both prime and composite (mutually exclusive definitions), and 1 is neither.

Common mistakes

  • Assuming all even numbers are composite (2 is the exception).
  • Confusing "neither prime nor composite" (which applies only to 1) with 2.

Common Mistakes

  1. 1Thinking 2 is composite because it is even — evenness alone does not make a number composite; 2 is the sole exception.
  2. 2Confusing the status of 1 with 2 — it is 1 that is neither prime nor composite, not 2.
  3. 3Believing a number can be both prime and composite; the two definitions are mutually exclusive.

Interesting Facts

2 is the only even prime number; all other primes (3, 5, 7, 11, ...) are odd, which is why 2 is sometimes called 'the oddest prime'.

The number 1 is deliberately excluded from primes so that the Fundamental Theorem of Arithmetic gives a UNIQUE factorisation — if 1 were prime, 6 could be written as 2×32\times3, 1×2×31\times2\times3, 1×1×2×31\times1\times2\times3, and so on.

The ancient Greek mathematician Eratosthenes (c. 240 BCE) devised the 'Sieve of Eratosthenes' to list primes, and 2 is always the first number circled.

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Frequently Asked Questions

Why is 2 a prime number even though it is even?

A number is prime if it has exactly two factors, 1 and itself, regardless of whether it is odd or even. The factors of 2 are only 1 and 2, so it is prime. It just happens to be the unique even prime; every larger even number has 2 as an additional factor and is composite.

Which number is neither prime nor composite?

The number 1 is neither prime nor composite, because it has only one factor (itself). A prime needs exactly two factors and a composite needs more than two, and 1 fits neither definition.

Can a number be both prime and composite?

No. 'Prime' means exactly two factors and 'composite' means more than two factors; a single number cannot satisfy both conditions, so the two categories never overlap.