The number whose only factors are 1 and the number itself is called a/an ________ number.
prime
Understanding Number Classification: Prime vs. Composite
The question asks us to identify the type of number that has only two factors: 1 and the number itself. Let's examine the options provided and the definition of each type of number.
Definition of Key Number Types
- Prime Number: A natural number greater than 1 that has no positive divisors other than 1 and itself.
- Composite Number: A natural number greater than 1 that is not prime. It has at least one divisor other than 1 and itself.
- Odd Number: An integer that is not divisible by 2. When divided by 2, it leaves a remainder of 1.
- Even Number: An integer that is divisible by 2, leaving no remainder.
Analyzing the Options
Based on the definitions, let's see which term fits the description "The number whose only factors are 1 and the number itself".
| Option | Definition Relevant to Factors | Matches the Description? |
|---|---|---|
| Prime | Has only two factors: 1 and itself. | Yes |
| Composite | Has factors other than 1 and itself. | No |
| Odd | Relates to divisibility by 2, not the total number of factors. | No |
| Even | Relates to divisibility by 2; most even numbers (except 2) have more than two factors. | No |
The definition provided in the question perfectly matches the definition of a prime number. For example, the number 7 has only two factors: 1 and 7. Similarly, 13 has only two factors: 1 and 13. Both 7 and 13 are prime numbers.
Examples to Illustrate
- Prime Numbers: 2 (factors: 1, 2), 3 (factors: 1, 3), 5 (factors: 1, 5), 7 (factors: 1, 7), 11 (factors: 1, 11).
- Composite Numbers: 4 (factors: 1, 2, 4), 6 (factors: 1, 2, 3, 6), 8 (factors: 1, 2, 4, 8), 9 (factors: 1, 3, 9), 10 (factors: 1, 2, 5, 10).
- Odd Numbers: 1, 3, 5, 7, 9, 11... (Some are prime, some are composite)
- Even Numbers: 2, 4, 6, 8, 10, 12... (Only 2 is prime; all other even numbers greater than 2 are composite)
Therefore, the number whose only factors are 1 and the number itself is called a prime number.
Revision Table: Number Properties
| Number Type | Definition by Factors | Other Key Property | Example(s) |
|---|---|---|---|
| Prime | Exactly two factors: 1 and itself. | > 1 and not divisible by any number other than 1 and itself. | 2, 3, 5, 7, 11 |
| Composite | More than two factors. | > 1 and has at least one factor other than 1 and itself. | 4, 6, 8, 9, 10 |
| Odd | Factors vary. | Not divisible by 2. | 1, 3, 5, 9, 15 |
| Even | Factors vary. | Divisible by 2. | 2, 4, 6, 8, 12 |
Additional Information on Prime Numbers
Prime numbers are fundamental building blocks in number theory. Every integer greater than 1 is either a prime number itself or can be represented as a product of prime numbers (this is known as the Fundamental Theorem of Arithmetic).
- The number 1 is neither prime nor composite. It has only one factor (1).
- The number 2 is the smallest and the only even prime number.
- There are infinitely many prime numbers (proven by Euclid).
- Identifying large prime numbers is important in cryptography.
Important Questions from Prime Numbers
Consider the following numbers :
1. 437
2. 797
3. 1073
How many of the above numbers are prime ?
What are the total prime numbers from 1 to 100?
How many prime numbers are there between 20 and 50?
How many prime numbers are there between 100 and 120?
The number 323 has
