Is 1335 a Prime Number?

There are two main types of numbers — 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 1335 has more than two factors, it is not a prime number.
   
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The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1335 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 numbers as prime and composite.

• 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 1335 is prime or composite

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

Step 2: Divide 1335 by 2. It is not divisible by 2, so 2 is not a factor of 1335.

Step 3: Divide 1335 by 3. The sum of the digits (1+3+3+5 = 12) is divisible by 3, so 3 is a factor of 1335.

Step 4: Further divisibility checks up to the square root of 1335 show additional factors.

Since 1335 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 or not. It is called the Divisibility Test Method. 

Divisibility by 2: 1335 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits (1+3+3+5 = 12) is divisible by 3, so 1335 is divisible by 3. 

Divisibility by 5: The unit’s place digit is 5, so 1335 is divisible by 5.

Divisibility by 7, 11, etc., shows additional factors.

Since 1335 is divisible by more than 2 numbers, it is 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 in a range such as 1 to 1000.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 as a prime number and cross out all multiples of 2.

Step 4: Mark 3 as a prime number and cross out all multiples of 3.

Step 5: Repeat until you have marked all prime numbers up to a certain limit.

Through this process, we find that 1335 is not in the list of prime numbers, confirming it is composite.

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

Step 1: We can write 1335 as 3 × 445. 
 

Step 2: Break down 445 further into 5 × 89. 
 

Step 3: 89 is a prime number. Therefore, the prime factorization of 1335 is 3 × 5 × 89.

• 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 it 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 4 are 1, 2, and 4 because they divide 4 completely. 

• Divisibility rules: Guidelines used to determine whether a number is divisible by another number without performing division. 

• Prime factorization: The process of expressing a number as the product of its prime factors.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit by iteratively marking the multiples of each prime starting from 2.