Is 273 a Prime Number?

No, 273 is not a prime number because it can be divided by more than two numbers

Prime numbers are the numbers which are divisible by only 1 and itself. As 273 does not meet the definition of prime number, 273 is not a prime number. The following are the methods to be used to find whether 273 is a prime number or not. 

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

In this method, we will find out the number of divisors which can divide the given number evenly. Based on the count of divisors, we will categorize the number as either prime or composite.

If the count of divisors is 2 then the number is a prime number.  

If the count of divisors is more than 2 then the number is a composite number.

Step 1: Note that, not only 273 but also every number is divisible by 1.

Step 2: Start dividing 273 by 2 and it cannot be divided by 2. So 2 is not a factor of 273.

Step 3: Then divide 273 by 3 and it can be divided by 3. So 3 is a factor of 273.

Step 4: Likewise, we have to divide the number by the numbers from 2 to the square root of that number.

√273=16.52 = 17 (approximately)

Step 5: As we can find that 273 is divisible by only 3, 7, and 13 when it is divided by the numbers from 2 to 17.

273 is not a prime number because 273 has more than 2 divisors.
 

A divisibility test is a method to check whether a number is divisible by another number or not. To perform this method, we need to divide the number by numbers from 1 to the square root of that number.

Here, 273 is divisible by more than 2 numbers which makes 273, a composite number.
 

Listing the prime numbers till 273: 2, 3, 5, 7, 11,13,17,19,23,29,31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,109, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179,181, 191, 193, 197.

273 is not among the numbers in the prime number chart. Therefore, 273 is a composite number.
 

Prime factorization is the method in which a number can be represented as a product of its prime factors. In this method we break down the number into its prime factors whose product will be obtaining the original number.

The prime factorization for 273 is 3 × 7 × 13.
 

• Prime numbers: The numbers which are greater than 1 and have only two factors are called prime numbers. For example, 2, 3, 5, 7, 11, 13, ……….are prime numbers.

• Factor: A number which can be multiplied by another number in order to obtain the required number. For example, 4 and 3 can be multiplied together to obtain 12. Hence, 4 and 3 can be considered as factors of 12.

• Divisibility: The property of a number that can be evenly divisible by another number.For example, 12 can be divisible by 1, 2, 3, 4, 6 and 12.

• Prime number chart: The chart which includes only prime numbers is called a Prime number chart.For example, a list including 2, 3, 5, 7, 11, 13, 17, 19 can be called a prime number chart.