Is 713 a Prime Number?

There are two main types of numbers

• 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 have specific 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. As 713 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 713 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. Some of these 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 713 is prime or composite.

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

Step 2: Divide 713 by 2. It is not divisible by 2, so 2 is not a factor of 713.

Step 3: Divide 713 by 3. It is not divisible by 3, so 3 is not a factor of 713.

Step 4: You can simplify checking divisors up to 713 by finding the square root value. We then need to check divisors up to the square root value.

Step 5: When dividing 713 by 2, 3, 5, 7, 11, and 13, it is found to be divisible by 23 and 31.

Since 713 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: 713 is not divisible by 2, as the last digit is not even.

Divisibility by 3: The sum of the digits in 713 is 11. Since 11 is not divisible by 3, 713 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5. Therefore, 713 is not divisible by 5.

Divisibility by 7: Performing the divisibility test for 7, 713 does not meet the criteria.

Divisibility by 11: Following the divisibility rule for 11, 713 does not meet the criteria. Since 713 has multiple factors besides 1 and itself, 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 from 1 to 1000 in a grid.

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 reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers. 713 is not present in this list, indicating it is a composite number.

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

Step 1: We can write 713 as 23 × 31.

Step 2: Both 23 and 31 are prime numbers. Hence, the prime factorization of 713 is 23 × 31.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 713 is a composite number because it is divisible by 1, 23, 31, and 713.
   
• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 23 is a prime number.
   
• Factors: The numbers that divide the given number exactly without leaving a remainder are called factors. For example, the factors of 713 are 1, 23, 31, and 713.
   
• Divisibility rules: Guidelines to determine if one number is divisible by another without performing division.
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 713 is 23 × 31.