Is 628 a Prime Number?

Numbers are classified as either prime numbers or 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 has more than two divisors. For example, 6 is divisible by 1, 2, 3, and 6, making it a composite number.

Properties of prime numbers include:

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.

Since 628 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 628 has more than two factors, it is not a prime number. Several methods are used to differentiate between prime and composite numbers, including:

• 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, numbers are categorized as follows:

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 628 is prime or composite.

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

Step 2: Divide 628 by 2. It is divisible by 2, so 2 is a factor of 628.

Step 3: Divide 628 by 3, 4, 5, and so on, up to the square root of 628. Since 628 is divisible by numbers other than 1 and itself, it has more than 2 divisors, making it a composite number.

The divisibility test method uses a set of rules to check whether a number is divisible by another number completely or not.

Divisibility by 2: The last digit of 628 is 8, which is an even number, so 628 is divisible by 2.

Divisibility by 3: The sum of the digits in 628 is 16. Since 16 is not divisible by 3, 628 is not divisible by 3.

Divisibility by 5: The last digit is 8, which is not 0 or 5, so 628 is not divisible by 5.

Divisibility by 7, 11, etc., can be checked similarly. Since 628 is divisible by numbers other than 1 and itself, it has more than two factors, making it a composite number.

The prime number chart is a tool created using the method called “The Sieve of Eratosthenes.” In this method, the following steps are used:

Step 1: Write numbers from 1 to 1000 in a grid.

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

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

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

Step 5: Repeat this process for each number. Through this process, you will have a list of prime numbers. Since 628 does not appear in the list of prime numbers, it is a composite number.

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

Step 1: Write 628 as 2 × 314.

Step 2: Further break down 314 into 2 × 157.

Step 3: Now, 157 is a prime number.

Therefore, the prime factorization of 628 is 2 × 2 × 157.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers. For example, 8 is a composite number because it is divisible by 1, 2, 4, and 8.

• Prime numbers: Natural numbers greater than 1 with exactly two distinct positive divisors: 1 and itself. For example, 11 is a prime number.

• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 10 are 1, 2, 5, and 10.

• Divisibility: The ability of one number to be divided by another without leaving a remainder. For example, 15 is divisible by 3.

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