Is 1267 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, which is 1.

To determine if 1267 is a prime number, we need to see if it has more than two factors.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1267 is not divisible by any other number besides 1 and 1267, it is a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

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

The method in which we count the number of divisors to categorize 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 is prime.

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

Let’s check whether 1267 is prime or composite:

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

Step 2: Check divisibility from 2 up to the square root of 1267.

Step 3: 1267 is not divisible by any number other than 1 and 1267 itself.

Since 1267 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.

- Divisibility by 2: 1267 is odd, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits in 1267 is 16, which is not divisible by 3.

- Divisibility by 5: The unit’s place digit is not 0 or 5, so it is not divisible by 5.

- Divisibility by 7, 11, 13, etc.: Performing specific checks shows that 1267 is not divisible by these numbers.

Since 1267 is not divisible by any number other than 1 and itself, it is a prime number.

The prime number chart is a tool created using a method called "The Sieve of Eratosthenes." In this method, we follow these steps:

Step 1: Write numbers up to a certain limit.

Step 2: Mark the first prime number and cross out all its multiples.

Step 3: Repeat for the next unmarked number.

Step 4: Continue until all numbers are marked or crossed out. Prime numbers up to 100 include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc. For numbers beyond 100, like 1267, we need to verify against divisibility rules.

Since 1267 is not divisible by any smaller prime numbers, it is confirmed as prime.

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

- Since 1267 is not divisible by any prime numbers up to its square root, it cannot be factored further into other primes.

- Thus, the prime factorization of 1267 is simply 1267 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
  
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers.
  
   
• Divisibility test: A set of rules to determine if one number is divisible by another without performing division.
  
   
• Prime factorization: Expressing a number as the product of its prime factors.
  
   
• Co-prime numbers: Two numbers with no common factors other than 1.