- The natural number 2 is : (a) a prime number (b) a composite number (c) prime as well as composite (d) neither prime nor composite
- The natural number 2 is : (a) a prime number (b) a composite number (c) prime as well as composite (d) neither prime nor composite
Options
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.
Marking scheme
- 1.1 mark: correct option (a) a prime number.
- 2.Expected 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.
Common mistakes
- 1.Thinking 2 is composite because it is even — evenness alone does not make a number composite; 2 is the sole exception.
- 2.Confusing the status of 1 with 2 — it is 1 that is neither prime nor composite, not 2.
- 3.Believing a number can be both prime and composite; the two definitions are mutually exclusive.
Analysis and 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.
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 , , , 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.
Question details
Q2 of 53 questions
- Board
- CBSE
- Class
- Class 10
- Subject
- Mathematics (Basic)
- Year
- 2026
- Section
- Section A
- Marks
- 1
- Type
- MCQ
- Chapter
- Real Numbers
- Topic
- Prime and composite numbers
- Bloom's level
- understand
- Syllabus topic
- Unit 1: Number Systems — Real Numbers: Prime and Composite Numbers
- Author
- CBSE
- Reviewed by
- Padhantu Academic Team
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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.