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
(a) a prime number — 2 has exactly two factors, 1 and 2, and is the only even prime number.
Marking Scheme
- 11 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.
Analysis & 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.
Common Mistakes
- 1Assuming all even numbers are composite and hence classifying 2 as composite.
- 2Confusing the number 1 (neither prime nor composite) with 2.
- 3Believing prime numbers must always be odd.
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.
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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.