Is 393 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 393 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 393 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:

• Counting Divisors Method

• Divisibility Test

• Prime Number Chart

• 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 and 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 393 is prime or composite.

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

Step 2: Divide 393 by 2. It is not divisible by 2 since 393 is odd.

Step 3: Divide 393 by 3. The sum of the digits is 15, which is divisible by 3, hence 393 is divisible by 3.

Step 4: You can simplify checking divisors up to 393 by finding the square root value. We then need to only check divisors up to the square root value.

Step 5: When we divide 393 by 3, we find it is divisible by 3 and 131.

Since 393 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. It is called the Divisibility Test Method.

Divisibility by 2: 393 is not divisible by 2 as it is odd.

Divisibility by 3: The sum of the digits in the number 393 is 15. Since 15 is divisible by 3, 393 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 393 is not divisible by 5.

Divisibility by 7: Double the last digit (3 × 2 = 6) and subtract it from the rest of the number (39 - 6 = 33). Since 33 is divisible by 3, 393 is also divisible by 3, but not by 7.

Divisibility by 11: In 393, the sum of the digits in odd positions is 6, and the sum of the digits in even positions is 9. The difference is 3, which is not divisible by 11. Since 393 is divisible by 3, it has more than two factors.

Therefore, it is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow the following steps.

Step 1: Write 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 without coloring or crossing, 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. The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 393 is not present in the list of prime numbers, so it is a composite 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: Start with the smallest prime number, which is 2, but since 393 is odd, it is not divisible by 2.

Step 2: Try dividing by 3. Since 393 is divisible by 3, we can write 393 as 3 × 131.

Step 3: 131 is a prime number. Hence, the prime factorization of 393 is 3 × 131.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 393 is a composite number because it is divisible by 1, 3, 131, and 393.

• Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of 393 is 3 × 131.

• Divisibility rules: Guidelines that help determine whether a number is divisible by another number. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

• Sieve of Eratosthenes: A method used to find all prime numbers up to a certain number by systematically marking the multiples of each prime number starting from 2.

• Co-prime numbers: Two numbers that have only 1 as their common divisor. For example, 8 and 15 are co-prime numbers because their greatest common divisor is 1.