Is 1316 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 1316 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 1316 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some methods include:

• 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 1316 is prime or composite.

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

Step 2: Divide 1316 by 2. It is divisible by 2, so 2 is a factor of 1316.

Step 3: Simplify checking divisors up to the square root of 1316.

Step 4: Continue checking divisibility with other numbers up to the square root. Since 1316 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 one's place value is 6, which is even, so 1316 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1316 is 11, which is not divisible by 3, so 1316 is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1316 is not divisible by 5.

Divisibility by 7: Apply the divisibility rule for 7 if needed.

Divisibility by 11: Apply the divisibility rule for 11 if needed. Since 1316 is divisible by 2, 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 range, for example, 1 to 1000.

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 other numbers. Through this process, we can identify prime numbers within a range. 1316 is not present in the list of prime numbers, so it is a composite number.

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

Step 1: We can write 1316 as 2 × 658.

Step 2: In 2 × 658, 658 can be further factorized into 2 × 329.

Step 3: 329 can be further factorized into 7 × 47. The prime factorization of 1316 is 2 × 2 × 7 × 47.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Divisibility rules: Set of rules to determine if one 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.