Is 397 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 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 that is 1.

As 397 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 397 has exactly two factors, it is a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are:

• 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 prime and composite numbers.

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 397 is prime or composite.

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

Step 2: Divide 397 by 2. It is not divisible by 2, so 2 is not a factor of 397.

Step 3: Divide 397 by 3. The sum of the digits (3 + 9 + 7 = 19) is not divisible by 3, so 3 is not a factor of 397.

Step 4: You can simplify checking divisors up to 397 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 397 by 5, 7, 11, 13, 17, 19, etc., it is not divisible by any of these. Since 397 has only 2 divisors, it is a prime 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: The number in the ones' place value is 7. Since 7 is odd, 397 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 397 is 19. Since 19 is not divisible by 3, 397 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 397 is not divisible by 5.

Divisibility by 7: The last digit in 397 is 7. To check divisibility by 7, double the last digit (7 × 2 = 14). Then, subtract it from the rest of the number (39 - 14 = 25). Since 25 is not divisible by 7, 397 is also not divisible by 7.

Divisibility by 11: In 397, the alternating sum of the digits is 3 - 9 + 7 = 1. This means that 397 is not divisible by 11. Since 397 is not divisible by any number other than 1 and itself, it is a prime 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 numbers in a grid format for easy reference.

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 for prime numbers up to the square root of the highest number in your range. Through this process, we will have a list of prime numbers. 397 is found in the list of prime numbers, confirming it is 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.

Since 397 is a prime number, it cannot be broken down into smaller prime factors. The prime factorization of 397 is simply 397 itself.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers.

• Divisibility: The ability of one number to be divided by another without leaving a remainder.

• Co-prime numbers: Two numbers that have only 1 as their common factor.

• Perfect square: A number that is the square of an integer.