Is 1313 a Prime Number?

There are two types of numbers, mostly

• Prime numbers
   
• 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 1313 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 1313 has more than two factors, it is not a prime number. Few methods are 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 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 1313 is prime or composite.

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

Step 2: Divide 1313 by 2. It is not divisible by 2, so 2 is not a factor of 1313.

Step 3: Divide 1313 by 3. It is not divisible by 3, so 3 is not a factor of 1313.

Step 4: Check divisors up to the square root of 1313, approximately 36.3, so we check up to 36.

Step 5: When we divide 1313 by 11, it is divisible by 11. Since 1313 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. This is called the Divisibility Test Method.

Divisibility by 2: 1313 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1313 is 8, which is not divisible by 3.

Divisibility by 5: 1313 does not end in 0 or 5, so it is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 1313 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is 1 - 3 + 1 - 3 = -4, which is divisible by 11. Since 1313 is divisible by 11, 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 sequence, say 1 to 100.

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 with the next unmarked number until you reach the desired range. Through this process, we will have a list of prime numbers in a given range. Since 1313 is not present in any 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 1313 as 11 × 119.

Step 2: In 11 × 119, 11 is a prime number. Further, break 119 into 7 × 17.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1313 is 11 × 7 × 17.

• 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.
   
• Prime numbers: Natural numbers greater than 1 that are divisible by only 1 and themselves. For example, 5 is a prime number.
   
• Divisibility rules: Guidelines to determine if one number is divisible by another number without performing division.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Co-prime numbers: Two numbers that have only one common factor, which is 1. For example, 8 and 15 are co-prime because their only common factor is 1.