What is a Factor?
A factor of a number divides the number completely, meaning it leaves no remainder. In other words, a certain number can be obtained by multiplying a pair of its factors. Consider the number 6; we can obtain the number six if we multiply 1 by 6 or by multiplying 2 by 3.
Division of 6 by 1, 2, 3 or 6 does not leave a remainder. That is because 1, 2, 3 and 6 are the factors of 6. We will get a remainder if we divide by any other number.
What is a Prime Number?
Prime numbers are numbers that have exactly two positive factors. One of the factors is 1 and the other factor is the number itself. Dividing a prime number with any number other than 1 and the number itself leaves a remainder. Some examples of prime numbers are 2, 3, 5, 7 and 11. The only factors of 2 are 1 and 2. Similarly, the factors of 3 are 1 and 3. The same rule is applicable to all prime numbers.
What is a Composite Number?
Composite numbers are numbers that have more than two positive factors. In other words, it is possible to divide a composite number by more than two numbers without leaving any remainder. A composite number leaves a remainder only if it is divided by a number that is not its factor. Every composite number can be expressed as the product of two prime numbers. Some examples of composite numbers are 4, 6, 8, 9 and 12. The factors of 4 are 1, 2 and 4, and the factors of 6 are 1, 2, 3 and 6. Similarly, all composite numbers have more than two positive factors.
Is 1 a Prime Number or a Composite Number?
The number 1 has only one factor: the number itself. Prime numbers have exactly two factors and composite numbers have more than two factors. So, it does not fit into the category of prime numbers or composite numbers. Hence, we can say that 1 is neither a prime number nor a composite number.
0 is neither a prime number nor a composite number. Even though any number multiplied by 0 is 0, it is not a composite number because it doesn’t have any prime factors.
Since 0 and 1 are not prime numbers, 2 is the smallest prime number. The factors of 2 are 1 and 2.
0 and 1 are neither prime nor composite. The numbers 2 and 3 are prime numbers. So, the smallest composite number is 4. The factors of 4 are 1, 2 and 4.