Question 21 markMCQSection A

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, and is the only even prime number.

Answer keywords:prime numbercomposite numbersmallest primeonly even primefactorsFundamental Theorem of Arithmetic

Marking scheme

  1. 1.1 mark for correctly identifying option (a) — 2 is a prime number.

Hint

Recall the definition: a prime number has exactly two factors, 1 and itself.

Quick oral answer

2 is a prime number — in fact it is the smallest prime and the only even prime, since it has exactly two factors, 1 and 2.

Common mistakes

  1. 1.Assuming all even numbers are composite and hence classifying 2 as composite.
  2. 2.Confusing the number 1 (neither prime nor composite) with 2.
  3. 3.Believing prime numbers must always be odd.

Analysis and explanation

Tests the basic definition of a prime number applied to the number 2.


Concept

  • A prime number has exactly two distinct positive factors: 1 and itself. 2 has only factors 1 and 2, so it is prime — and it is the only even prime.

Key points

  • A composite number has more than two factors (e.g., 4 → 1, 2, 4).
  • No number can be both prime and composite (mutually exclusive definitions).
  • 'Neither prime nor composite' applies only to the number 1, not to 2.

Common mistakes

  • Assuming all even numbers are composite, forgetting 2 is the exception.
  • Confusing 'neither prime nor composite' (true only for 1) with small numbers in general.

Real-world/exam link

  • This idea underlies the Fundamental Theorem of Arithmetic — every composite number is a unique product of primes, with 2 often the starting prime factor.

Interesting facts

2 is the only even prime number in all of mathematics — every other prime is odd.

The ancient Greek mathematician Euclid proved around 300 BCE that there are infinitely many prime numbers, a proof still taught today.

Question details

Q2 of 56 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Standard)
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Real Numbers
Topic
Prime and Composite Numbers
Bloom's level
remember
Syllabus topic
Unit 1: Number Systems — Real Numbers: Prime Numbers and the Fundamental Theorem of Arithmetic
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Why is 2 the only even prime number?

Every even number greater than 2 is divisible by 2 in addition to 1 and itself, giving it more than two factors, so it is composite. Only 2 itself has exactly two factors (1 and 2).

Is 1 a prime number?

No, 1 has only one factor (itself), so it does not meet the definition of a prime number requiring exactly two distinct factors; it is classified as neither prime nor composite.