Is 673 a Prime Number?

There are two main types of numbers—

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 integer that is divisible by more than two distinct numbers.

For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Prime numbers have the following properties:

• 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 we will explore, 673 has only two factors, making it a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 673 has exactly two factors, it is a prime number. Several methods help to distinguish between prime and composite numbers, such as:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. 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 is prime.

• If the count is more than 2, then the number is composite.

Let’s check whether 673 is prime or composite.

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

Step 2: Check divisibility of 673 by numbers up to its square root, which is approximately 25.9.

Step 3: 673 is not divisible by any integer other than 1 and 673.

Therefore, it is a prime number.

We use a set of rules to check whether a number is divisible by another number completely or not, called the Divisibility Test Method.

Divisibility by 2: 673 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 673 is 16, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is 3, so 673 is not divisible by 5.

Divisibility by 7, 11, 13, etc.: 673 is not divisible by these or any small primes up to the square root of 673.

Since 673 is not divisible by any smaller prime numbers, it is a prime 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 up to a certain limit.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all its multiples.

Step 4: Continue marking prime numbers and crossing out their multiples.

673 is a prime number as it is not crossed out in this sieve process, confirming it is not divisible by any other numbers except 1 and itself.

Prime factorization is a process of breaking down a number into prime factors. For 673:

Step 1: Attempt to divide 673 by small prime numbers such as 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Step 2: None of these divide 673 without a remainder. Thus, 673 cannot be factored into smaller prime numbers, confirming 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 is not prime, meaning it has more than two positive divisors.

• Divisibility: The ability of one integer to be divided by another without a remainder.

• Prime Factorization: The process of determining which prime numbers multiply together to make a given number.

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