Is 1289 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.
  
   
• As 1289 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 1289 has exactly two factors, it is a prime number. Several methods can be 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 1289 is prime or composite.
 

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

Step 2: Check divisibility of 1289 by prime numbers up to its square root.

Step 3: The square root of 1289 is approximately 35.9, so check divisibility by prime numbers up to 35.

Step 4: 1289 is not divisible by any prime numbers less than 35 (like 2, 3, 5, 7, 11, etc.).

Since 1289 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. This is called the Divisibility Test Method.

Divisibility by 2: The number in the ones' place value is 9, which is odd. Therefore, 1289 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1289 is 20. Since 20 is not divisible by 3, 1289 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 9, which does not end in 0 or 5. Therefore, 1289 is not divisible by 5.

Divisibility by 7: Using divisibility rules, 1289 is not divisible by 7.

Divisibility by 11: By applying the rules for 11, 1289 is not divisible by 11.

Since 1289 is not divisible by any smaller prime numbers, it has no divisors other than 1 and itself.

Thus, 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 rows and columns up to a certain limit.

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 for all numbers up to the square root of the maximum number in the table.

Through this process, we will have a list of prime numbers.

As 1289 is not divisible by any prime numbers up to its square root, it confirms that 1289 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: Check divisibility starting from the smallest prime number.

Step 2: 1289 is not divisible by 2, 3, 5, 7, 11, etc., up to its square root.

Step 3: Since 1289 cannot be broken down into smaller prime factors, it is itself a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and the number itself.
  
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers.
  
   
• Divisibility rules: Guidelines used to determine if a number is divisible by another without performing division.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
  
   
• Co-prime numbers: Two numbers that have only 1 as their common divisor.