Is 381 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 381 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 381 has more than two factors, it is not a prime number. A 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 381 is prime or composite.

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

Step 2: Divide 381 by 2. It is not divisible by 2, so 2 is not a factor of 381.

Step 3: Divide 381 by 3. It is divisible by 3, so 3 is a factor of 381.

Step 4: You can simplify checking divisors up to 381 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 381 by 3 and 127, it is divisible by both.

Since 381 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: The number in the ones' place value is 1. Since 1 is an odd number, 381 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 381 is 12. Since 12 is divisible by 3, 381 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 381 is not divisible by 5.

Divisibility by 7: The last digit in 381 is 1. To check divisibility by 7, double the last digit (1 × 2 = 2).

Then, subtract it from the rest of the number (38 - 2 = 36).

Since 36 is divisible by 7, 381 is divisible by 7.

Since 381 is divisible by 3 and 7, 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 numbers from 1 to 100 or higher, depending on the range you're interested in.

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. Since 381 is not on the list of prime numbers (between 1 to 100), it is a composite number.

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

Step 1: We can write 381 as 3 × 127.

Step 2: Both 3 and 127 are prime numbers.

Step 3: Therefore, the prime factorization of 381 is 3 × 127.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 381 is a composite number because it is divisible by 1, 3, 127, and 381.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 3 and 127 are prime numbers.

• Divisibility rules: A set of rules that help determine whether one number is divisible by another without performing full division.

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

• Odd numbers: Numbers not divisible by 2. For example, 381 is an odd number.