Is 328 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.
• As 328 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 328 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include: -

1. Counting Divisors Method 
2. Divisibility Test 
3. Prime Number Chart 
4. 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 numbers as prime or composite. 

• 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 328 is prime or composite.

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

Step 2: Divide 328 by 2. It is divisible by 2, so 2 is a factor of 328.

Step 3: Divide 328 by 3. It is not divisible by 3, so 3 is not a factor of 328.

Step 4: You can simplify checking divisors up to the square root of 328, which is approximately 18.

Step 5: When we divide 328 by 2, 4, 8, and 41, it is divisible by these numbers.

Since 328 has more than 2 divisors, it is a composite 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: The number in the ones' place is 8, which is even, meaning that 328 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 328 is 13. Since 13 is not divisible by 3, 328 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 8. Therefore, 328 is not divisible by 5. 

Divisibility by 7: The last digit in 328 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (32 - 16 = 16). Since 16 is not divisible by 7, 328 is also not divisible by 7. 

Divisibility by 11: In 328, the sum of the digits in odd positions is 11, and the sum of the digits in even positions is 2. The difference is 9, which means that 328 is not divisible by 11.

Since 328 is divisible by 2 and other factors, it has more than two factors. Therefore, it is a composite 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 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 without coloring or crossing it, 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 reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 328 is larger than 100, we can see it does not appear on the list of prime numbers up to 100, and further analysis shows it is not 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: We can write 328 as 2 × 164.

Step 2: In 2 × 164, 164 is a composite number. Further, break the 164 into 2 × 82.

Step 3: Now break down 82 into 2 × 41.

Step 4: 41 is a prime number. Hence, the prime factorization of 328 is 2 × 2 × 2 × 41.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 328 is a composite number because it is divisible by 1, 2, 4, 8, 41, 82, 164, and 328.

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

• Divisibility test: A method to determine if one number is divisible by another without performing actual division.

• Prime factorization: The process of expressing a number as the product of its prime factors.

• Factors: Numbers that divide the original number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.