Is 1355 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 1355 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 1355 has more than two factors, it is not a prime number. There are several methods 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 1355 is prime or composite.

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

Step 2: Divide 1355 by 5. It is divisible by 5, so 5 is a factor of 1355.

Step 3: Divide 1355 by 7. It is divisible by 7, so 7 is a factor of 1355.

Step 4: You can simplify checking divisors up to 1355 by finding the root value. We then need to only check divisors up to the root value.

Since 1355 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: The number in the ones' place value is 5. Five is an odd number, which means that 1355 is not divisible by 2.

- Divisibility by 3: The sum of the digits in the number 1355 is 14. Since 14 is not divisible by 3, 1355 is also not divisible by 3.

- Divisibility by 5: The unit’s place digit is 5. Therefore, 1355 is divisible by 5.

- Divisibility by 7: The last digit in 1355 is 5. Double the last digit (5 × 2 = 10). Subtract it from the rest of the number (135 - 10 = 125). Since 125 is divisible by 7, 1355 is also divisible by 7.

- Divisibility by 11: In 1355, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 8. This would mean that 1355 is not divisible by 11.

Since 1355 is divisible by both 5 and 7, it has more than two factors. Therefore, it is a composite 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 a structured format 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 until you mark all prime numbers in your list. Through this process, we will have a list of prime numbers.

Since 1355 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 prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 1355 as 5 × 271.

Step 2: In 5 × 271, both 5 and 271 are prime numbers.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1355 is 5 × 271.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1355 is a composite number because it is divisible by 1, 5, 271, and 1355.
  
   
• Divisibility rules: A set of guidelines that help determine if one number is divisible by another without performing division.
  
   
• Prime factorization: The process of breaking down a composite number into the product of its prime numbers.
  
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.
  
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 1355 are 1, 5, 271, and 1355.