Is 622 a Prime Number?

Numbers are categorized into two types, primarily —

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 instance, 3 is a prime number because it is divisible by 1 and 3.

A composite number is a positive number that has more than two divisors.

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

Prime numbers have certain properties such as:

• Prime numbers are positive numbers greater than 1.
   
• 2 is the only even prime number.
   
• They have exactly 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 622 has more than two factors, it is not a prime number.
  

A prime number is defined by having only two divisors: 1 and itself. Since 622 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, such as:

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

The counting divisors method involves identifying the number of divisors a number has to determine whether it is prime or composite. Based on the count of the divisors: If there are only 2 divisors, the number is prime. If there are more than 2 divisors, the number is composite. Let’s check whether 622 is prime or composite.

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

Step 2: Divide 622 by 2. It is divisible by 2, so 2 is a factor of 622.

Step 3: Divide 622 by 3. It is not divisible by 3, so 3 is not a factor of 622.

Step 4: Simplify checking divisors up to the square root of 622.

Step 5: When we divide 622 by 2, 311, and other numbers, it is divisible by 2 and 311.

Since 622 has more than 2 divisors, it is a composite number.

The Divisibility Test Method uses rules to verify if a number is divisible by another number without leaving a remainder.

Divisibility by 2: The ones' place digit of 622 is 2, which is even, so 622 is divisible by 2.

Divisibility by 3: The sum of the digits in 622 is 10. Since 10 is not divisible by 3, 622 is not divisible by 3.

Divisibility by 5: The units digit is not 0 or 5, so 622 is not divisible by 5.

Divisibility by 7: Calculating further shows it is not divisible by 7.

Since 622 is divisible by 2 and 311, it has more than two factors, making it a composite number.

The prime number chart, developed using the “Sieve of Eratosthenes,” assists in identifying prime numbers.

Step 1: Write numbers from 1 to 100 in a grid format.

Step 2: Leave 1 uncolored, as it is neither prime nor composite.

Step 3: Mark 2 as prime and cross out all multiples of 2.

Step 4: Mark 3 as prime and cross out all multiples of 3.

Step 5: Continue this process up to 100. From this, we get a list of prime numbers up to 100.

As 622 is not in this range and not in the list of prime numbers, it is composite.

Prime factorization breaks down a number into its prime factors.

Step 1: Express 622 as 2 × 311.

Step 2: Both 2 and 311 are prime numbers.

Therefore, the prime factorization of 622 is 2 × 311.

• Composite numbers: Natural numbers greater than 1 that have more than two factors are called composite numbers. For example, 12 is a composite number because it has factors of 1, 2, 3, 4, 6, and 12.
   
• Co-prime numbers: Two numbers are co-prime if their only common factor is 1.
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division.
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
   
• Sieve of Eratosthenes: A method used to find all prime numbers up to a certain limit by systematically marking the multiples of each prime number starting from 2.