Is 1359 a Prime Number?

There are two main types of numbers — prime numbers and composite numbers, determined by the number of factors they have.

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 have a few properties, such as:

- 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.

Since 1359 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1359 has more than two factors, it is not a prime number. There are a few methods used to distinguish between prime and composite numbers, including:

• 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 1359 is prime or composite.

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

Step 2: Divide 1359 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 1359 by 3. The sum of the digits (1 + 3 + 5 + 9 = 18) is divisible by 3, so 1359 is divisible by 3.

Step 4: You can simplify checking divisors up to 1359 by finding the root value. We only need to check divisors up to the approximate square root of 1359, which is about 36.

Step 5: Continue testing divisibility by other numbers such as 5, 7, etc. 1359 is divisible by 3, 11, and 41.

Since 1359 has more than 2 divisors, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely. This is called the Divisibility Test Method.

Divisibility by 2: The last digit of 1359 is 9, which is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1359 is 18, which is divisible by 3.

Divisibility by 5: The last digit is not 0 or 5, so it is not divisible by 5.

Divisibility by 7: Calculate 135 - (2×9) = 117, which is not divisible by 7.

Divisibility by 11: The alternating sum of digits (1 - 3 + 5 - 9 = -6) is not divisible by 11.

Divisibility by 41: Direct division shows 1359 is divisible by 41.

Since 1359 is divisible by multiple numbers, it has more than two factors and is therefore a composite 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 from 1 to 100 (or more) in rows and columns.

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 have a table of marked and crossed boxes, except 1. Through this process, we have a list of prime numbers.

Since 1359 is not present in the list of prime numbers, it is a composite number.

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

Step 1: We can write 1359 as 3 × 453.

Step 2: In 3 × 453, 453 is a composite number. Further, break down 453 into 3 × 151.

Step 3: 151 is a prime number, so the prime factorization of 1359 is 3 × 3 × 151.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1359 is a composite number because it is divisible by 1, 3, 7, 21, 41, 123, 453, and 1359.
  
   
• Divisibility test: A method to determine if one number is divisible by another without performing full division.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
  
   
• Co-prime numbers: Two numbers that have only 1 as their common factor.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specific integer.