Is 683 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.

To determine if 683 is a prime number, we will examine its factors.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 683 has more than two factors, it is not a prime number. A 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 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 683 is prime or composite.

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

Step 2: Divide 683 by numbers starting from 2 up to the square root of 683, approximately 26.

Step 3: 683 is not divisible by any number other than 1 and itself without leaving a remainder.

Since 683 has only two divisors, it is a prime 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: 683 is not divisible by 2 as it is an odd number.

Divisibility by 3: The sum of the digits in 683 is 17, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3, so 683 is not divisible by 5.

Divisibility by other small primes like 7, 11, 13, 17, 19, 23, and 29 also results in remainders. Since 683 is not divisible by any number other than 1 and itself, it is a prime 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 manageable range.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark multiples of each prime number starting with 2.

Step 4: Continue this process until you cover the desired range. Through this process, we will have a list of prime numbers.

Since 683 is not in the list of any composite numbers up to its square root, it is a prime 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: Check divisibility by prime numbers starting from 2 up to the square root.

Step 2: If no prime numbers divide 683 without a remainder, it is a prime number.

Since 683 cannot be factored into smaller primes, it is a prime number.

• Prime number: A natural number greater than 1 that has no positive divisors other than 1 and itself.

• Composite number: A natural number greater than 1 that has more than two positive divisors.

• Divisibility: A situation in which one integer can be divided by another without leaving a remainder.

• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to a specified integer.

• Co-prime numbers: Two numbers that have no common factors other than 1.