Is 1373 a Prime Number?

There are two types of numbers, mostly —

Prime numbers and composite numbers, depending on the number of factors.

A prime number is a natural number that is divisible only by 1 and itself.

For example, 5 is a prime number because it is divisible by 1 and itself.

A composite number is a positive number that is divisible by more than two numbers.

For example, 8 is divisible by 1, 2, 4, and 8, making it a composite number.

Prime numbers follow a few properties like:

• Prime numbers are positive numbers always greater than 1.
   
• 2 is the only even prime number.
   
• They have only two factors: 1 and the number itself.
   
• Any two distinct prime numbers are co-prime numbers because they have only one common factor, which is 1.
  
  As 1373 has only two factors, it is a prime number.
  
  

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1373 has exactly two factors, it is a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are:
 

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization
   

The method in which we count the number of divisors to categorize the numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize prime and composite numbers.

If there is a total count of only 2 divisors, then the number would be prime.

If the count is more than 2, then the number is composite.
 

Let’s check whether 1373 is prime or composite.

Step 1: All numbers are divisible by 1 and itself.

Step 2: Divide 1373 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Continue dividing 1373 by subsequent numbers (3, 5, 7, etc.) up to the square root of 1373, which is approximately 37.

Step 4: None of these numbers divides 1373 without leaving a remainder.

Since 1373 has only 2 divisors (1 and 1373 itself), it is a prime number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: 1373 is not divisible by 2, as it is an odd number.

Divisibility by 3: The sum of the digits in the number 1373 is 14. Since 14 is not divisible by 3, 1373 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 1373 is not divisible by 5.

Divisibility by 7, 11, etc.: Applying tests for these and other numbers up to the square root of 1373 shows that 1373 is not divisible by any of them.

Since 1373 is not divisible by any number other than 1 and itself, it is a prime number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps:

Step 1: Write a list of numbers, say from 1 to 1000.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until you reach the highest number in your list. Through this process, we will have a list of prime numbers.

Since 1373 is not divisible by any smaller primes, it confirms 1373 as a prime number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: Start with the smallest prime number, which is 2, and go up to the square root of 1373.

Step 2: Try dividing 1373 by each prime number.

Step 3: 1373 is not divisible by any smaller prime numbers without leaving a remainder.

Since there are no smaller prime factors, 1373 itself is prime.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 8 are 1, 2, 4, and 8 because they divide 8 completely.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all primes up to a specified integer by iteratively marking the multiples of each prime starting from 2.
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.