To determine the correct definition of a prime number among the provided options, we'll examine each choice carefully.
1. A number that is divisible only by itself and 1
- This definition accurately describes a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, the number 7 is divisible only by 1 and 7.
2. A number that is divisible only by itself
- This choice is misleading because prime numbers must also be divisible by 1. For example, the number 7 would not be considered prime by this definition, as it must also consider 1 as a divisor.
3. A number that is not a product of two numbers
- This is a false statement. Prime numbers can indeed be expressed as a product of two numbers: 1 and the number itself.
4. A number that is the product of composite numbers
- This definition is incorrect. Prime numbers, by definition, cannot be the product of composite numbers. Composite numbers are those that have divisors other than 1 and themselves, such as 4, 6, 8, etc.
Given these evaluations, the correct choice and the true definition of a prime number is:
0. A number that is divisible only by itself and 1
