Is -3 a prime number?

The number -3 has 2 factors: 1 and -3. However, prime numbers are typically defined as positive integers greater than 1, so -3 is not considered a prime number. Prime numbers are positive and greater than 1.

A number to be a prime number should follow the criteria that it must be positive and greater than 1, and it should not have more than 2 factors. Since -3 is a negative number, it doesn't meet the criteria of a prime number.

Given below are a few ways that can be used to find prime or composite numbers.

The different methods we can use to check if a number is a prime number are explained below.

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization
    

For the counting divisors method, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for -3 would simply be

Divisors of -3 = 1, -3
Number of divisors = 2

Since prime numbers are defined as positive numbers greater than 1, -3 cannot be considered a prime number.
 

In the division test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

In the divisibility method, the prime number only has 2 divisors, which are 1 and itself.

The divisors of -3 are 1 and -3, but as -3 is a negative number, it doesn't meet the criteria for a prime number.
 

The prime number chart is the list of prime numbers starting from 2 to infinity.

The list of prime numbers under 100 are;

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

-3 is not present in the list, as prime numbers are positive, and -3 is negative.

This method is only used for a non-prime number/composite number. Since -3 is not a prime number, prime factorization doesn't apply in the same way. However, you could express -3 as a product of 1 and -3, but this is not typical prime factorization.
 

• Prime Number: A positive integer greater than 1 that has exactly two distinct divisors: 1 and itself. Example: 2, 3, and 5 are prime numbers.

• Divisors: The numbers that can divide a given number without leaving a remainder. For example, the divisors of 6 are 1, 2, 3, and 6.

• Composite Number: A positive integer greater than 1 that has more than two distinct divisors. For example, 4, 6, and 8 are composite numbers.

• Divisibility Test: A method used to determine if a number is divisible by another number. In this context, we check if the number can be divided by prime numbers like 2, 3, 5, etc.

• Negative Numbers: Numbers less than zero. Negative numbers, like -3, do not meet the criteria for being prime, as prime numbers must be positive integers greater than 1.