Is 607 a Prime Number?

There are primarily two types of numbers —

prime numbers and composite numbers, based on the number of factors they have.

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 certain 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 607 has only two factors, it is a prime number.
  

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 607 does not have more than two factors, it is a prime number. Several methods can be used to distinguish between prime and composite numbers, including: 

• 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 numbers as prime or composite. - If there is a total count of only 2 divisors, the number is prime. - If the count is more than 2, the number is composite. Let’s check whether 607 is prime or composite.

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

Step 2: Check divisibility by numbers up to the square root of 607 (approximately 24.6). Only check divisors that are prime numbers. After checking, 607 is not divisible by any prime numbers up to its square root.

Since 607 has only 2 divisors (1 and 607), it is a prime 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: 607 is odd, and thus not divisible by 2.

Divisibility by 3: The sum of the digits (6 + 0 + 7 = 13) is not divisible by 3.

Divisibility by 5: The unit's place digit is 7, not 0 or 5, so 607 is not divisible by 5. 

Divisibility by 7, 11, 13, etc.: Applying similar rules, 607 is not divisible by these numbers.

Since 607 is not divisible by any numbers other than 1 and 607 itself, 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 to 1000 in rows and columns.

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 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 have marked all prime numbers. Through this process, we can identify that 607 is a prime number as it remains unmarked.

Prime factorization is a process of breaking down a number into its prime factors. Then multiply those factors to obtain the original number.

Step 1: Attempt to divide 607 by the smallest primes (like 2, 3, 5, 7, etc.) up to its square root.

Step 2: When no division yields an integer, 607 is confirmed to have no prime factors other than itself.

Since 607 is only divisible by 1 and itself, it is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 5 is a prime number.
   
• Composite numbers: Natural numbers greater than 1 that have more than two factors. For example, 12 is a composite number because it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Divisibility rules: A set of rules that help determine if a number is divisible by another number without performing division.
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit by iteratively marking the multiples of each prime number.