Is 1367 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, 3 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, 6 is divisible by 1, 2, 3, and 6, 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 that is 1.

As 1367 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 1367 has exactly two factors, it is a prime number. A few methods can be used to distinguish between prime and composite numbers. Some 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 1367 is prime or composite.

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

- Step 2: Divide 1367 by numbers starting from 2 to the square root of 1367, which is approximately 36.9.

- Step 3: None of these numbers divides 1367 perfectly except 1 and 1367 itself.

Since 1367 has only 2 divisors, 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. Check divisibility by various numbers:

- Divisibility by 2: 1367 is an odd number, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits in the number 1367 is 17. Since 17 is not divisible by 3, 1367 is not divisible by 3.

- Divisibility by 5: The unit’s place digit is 7, so 1367 is not divisible by 5.

- Divisibility by 7, 11, 13, etc.: Testing shows 1367 is not divisible by any of these lower prime numbers.

Since 1367 is not divisible by any other number except 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 numbers in sequence up to a certain limit.

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

- Step 3: Mark small prime numbers like 2, 3, 5, and cross out all their multiples.

- Step 4: Continue this process up to the square root of the maximum number in your list. Through this process, a list of smaller primes can be used to verify larger numbers like 1367.

Since 1367 is not divisible by any smaller prime numbers, it confirms that 1367 is a prime number.

Prime factorization is a process of breaking down a number into prime factors. Then multiply those factors to obtain the original number.

- Step 1: Attempt to divide 1367 by smaller prime numbers like 2, 3, 5, 7, etc.

- Step 2: None of these divisions results in a whole number, confirming that 1367 itself is prime.

• Prime number: A number greater than 1 that has no divisors other than 1 and itself.
  
   
• Composite number: A natural number greater than 1 that is not prime, meaning it has more than two distinct divisors.
  
   
• Divisibility: The condition in which one number can be divided by another without leaving a remainder.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors.