Question:
The natural number 2 is :
The natural number 2 is :
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Remember that 2 is the only even prime number in existence.
All other even numbers greater than 2 have at least 1, 2, and themselves as factors, making them composite.
All other even numbers greater than 2 have at least 1, 2, and themselves as factors, making them composite.
Updated On: Jul 7, 2026
- a prime number
- a composite number
- prime as well as composite
- neither prime nor composite
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The topic of this question is the classification of natural numbers in the Real Number system.
We need to determine the mathematical classification of the number 2 among the given options.
Step 2: Key Formula or Approach:
We use the fundamental definitions of prime and composite numbers:
• A natural number $n \gt 1$ is a
prime number if its only positive divisors are 1 and $n$ itself.
• A natural number $n \gt 1$ is a
composite number if it has more than two positive divisors.
• The number 1 is unique as it has only one positive divisor and is classified as neither prime nor composite.
Step 3: Detailed Explanation:
• Let us write down all the factors (divisors) of the natural number 2.
The positive divisors of 2 are only 1 and 2.
• Since the number 2 has exactly two distinct positive divisors, namely 1 and the number itself, it perfectly satisfies the definition of a prime number.
• It does not satisfy the definition of a composite number, because it does not have any additional divisors.
• Thus, 2 cannot be both prime and composite, nor can it be categorized as neither.
• Additionally, 2 is historically significant as the smallest prime number and the only even prime number in the infinite set of prime numbers.
Step 4: Final Answer:
The natural number 2 is a prime number, corresponding to option (A).
The topic of this question is the classification of natural numbers in the Real Number system.
We need to determine the mathematical classification of the number 2 among the given options.
Step 2: Key Formula or Approach:
We use the fundamental definitions of prime and composite numbers:
• A natural number $n \gt 1$ is a
prime number if its only positive divisors are 1 and $n$ itself.
• A natural number $n \gt 1$ is a
composite number if it has more than two positive divisors.
• The number 1 is unique as it has only one positive divisor and is classified as neither prime nor composite.
Step 3: Detailed Explanation:
• Let us write down all the factors (divisors) of the natural number 2.
The positive divisors of 2 are only 1 and 2.
• Since the number 2 has exactly two distinct positive divisors, namely 1 and the number itself, it perfectly satisfies the definition of a prime number.
• It does not satisfy the definition of a composite number, because it does not have any additional divisors.
• Thus, 2 cannot be both prime and composite, nor can it be categorized as neither.
• Additionally, 2 is historically significant as the smallest prime number and the only even prime number in the infinite set of prime numbers.
Step 4: Final Answer:
The natural number 2 is a prime number, corresponding to option (A).
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