Is 1/3 a prime number?

The number 1/3 is a fraction, and prime numbers apply only to whole numbers (integers). Therefore, 1/3 cannot be considered a prime number. Prime numbers must be whole numbers with exactly two distinct positive divisors: 1 and the number itself. Since 1/3 is not a whole number, it does not meet the criteria for being prime.

A prime number must be a whole number greater than 1 that is divisible only by 1 and itself. Since 1/3 is a fraction and not a whole number, it does not qualify as a prime number.

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.

Since 1/3 is not a whole number, it has no whole-number divisors, and therefore cannot be considered prime.
 

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.

1/3 is not a whole number, so it doesn't pass the divisibility test for prime numbers.
 

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.

1/3 is not present in the list, as it is not a whole number.
 

This method is only used for a non-prime number/composite number. Since 1/3 is not a whole number, the prime factorization method does not apply.
 

• Prime Number: A whole number greater than 1 that is divisible only by 1 and itself, with exactly two distinct positive divisors. Examples include 2, 3, 5, 7, and 11.

• Whole Number: Any of the numbers in the set of natural numbers (0, 1, 2, 3, ...) that do not have any fractional or decimal parts. Prime numbers are always whole numbers.

• Fraction: A mathematical expression representing the division of one quantity by another, written in the form of "numerator/denominator." 1/3 is a fraction and cannot be prime, as prime numbers apply only to whole numbers.

• Divisibility Test: A method used to check whether one number is divisible by another without leaving a remainder. For prime numbers, this test helps confirm if the number can only be divided evenly by 1 and itself.

• Prime Factorization: The process of determining the prime numbers that multiply together to give a specific number. Since 1/3 is a fraction, this method does not apply to it.