Question:
The natural number 1 is :
The natural number 1 is :
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Remember that 2 is the smallest prime number and the only even prime number.
The number 1 is uniquely classified as a unit, making it the only positive integer greater than 0 that is neither prime nor composite.
The number 1 is uniquely classified as a unit, making it the only positive integer greater than 0 that is neither prime nor 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 D
Solution and Explanation
Step 1: Understanding the Question:
The question asks us to classify the natural number 1 into one of the standard categories of natural numbers: prime, composite, both, or neither.
Step 3: Detailed Explanation:
1. Let us define a
prime number:
A prime number is a natural number strictly greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, 5, 7, 11, etc.
Since the natural number 1 does not have two distinct divisors (its only divisor is 1 itself), it cannot be classified as a prime number.
2. Let us define a
composite number:
A composite number is a natural number that has more than two distinct positive divisors. Examples include 4, 6, 8, 9, 10, etc.
Since the natural number 1 has only one positive divisor (1), it does not satisfy the condition of having more than two divisors. Thus, it cannot be classified as a composite number.
3. In number theory, the number 1 is classified as a "unit" (a number with a multiplicative inverse in the ring of integers).
Because of this unique role, 1 is excluded from both the definition of prime numbers and composite numbers to ensure the uniqueness of the Prime Factorization Theorem (the Fundamental Theorem of Arithmetic). If 1 were considered prime, prime factorizations would not be unique (for example, \(6 = 2 \times 3 = 1 \times 2 \times 3 = 1^2 \times 2 \times 3\), etc.).
Therefore, the natural number 1 is neither prime nor composite.
Step 4: Final Answer:
The natural number 1 is neither prime nor composite, which corresponds to option (D).
The question asks us to classify the natural number 1 into one of the standard categories of natural numbers: prime, composite, both, or neither.
Step 3: Detailed Explanation:
1. Let us define a
prime number:
A prime number is a natural number strictly greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples include 2, 3, 5, 7, 11, etc.
Since the natural number 1 does not have two distinct divisors (its only divisor is 1 itself), it cannot be classified as a prime number.
2. Let us define a
composite number:
A composite number is a natural number that has more than two distinct positive divisors. Examples include 4, 6, 8, 9, 10, etc.
Since the natural number 1 has only one positive divisor (1), it does not satisfy the condition of having more than two divisors. Thus, it cannot be classified as a composite number.
3. In number theory, the number 1 is classified as a "unit" (a number with a multiplicative inverse in the ring of integers).
Because of this unique role, 1 is excluded from both the definition of prime numbers and composite numbers to ensure the uniqueness of the Prime Factorization Theorem (the Fundamental Theorem of Arithmetic). If 1 were considered prime, prime factorizations would not be unique (for example, \(6 = 2 \times 3 = 1 \times 2 \times 3 = 1^2 \times 2 \times 3\), etc.).
Therefore, the natural number 1 is neither prime nor composite.
Step 4: Final Answer:
The natural number 1 is neither prime nor composite, which corresponds to option (D).
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