Is 391 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 391 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 391 has more than two factors, it is not 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 391 is prime or composite.

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

Step 2: Divide 391 by 2. It is not divisible by 2, so 2 is not a factor of 391.

Step 3: Divide 391 by 3. It is not divisible by 3, so 3 is not a factor of 391.

Step 4: You can simplify checking divisors up to 391 by finding the root value, approximately 19.76. We then need to only check divisors up to the root value.

Step 5: When we divide 391 by 17, it is divisible, indicating 17 is a factor of 391. Since 391 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: 391 is odd and therefore not divisible by 2.

Divisibility by 3: The sum of the digits in the number 391 is 13. Since 13 is not divisible by 3, 391 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 391 is not divisible by 5.

Divisibility by 7: Double the last digit (1 × 2 = 2). Subtract it from the rest of the number (39 - 2 = 37). Since 37 is not divisible by 7, 391 is also not divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd positions (3+1=4) and the sum of the digits in even positions (9) is 5. This means that 391 is not divisible by 11. Since 391 is divisible by 17, 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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all 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. 391 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: We can write 391 as 17 × 23.

Step 2: Both 17 and 23 are prime numbers.

Therefore, the prime factorization of 391 is 17 × 23.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 391 is a composite number because it is divisible by 1, 17, 23, and 391.

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

• Divisibility rules: Guidelines to determine if a number is divisible by another without performing the actual division.

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

• Co-prime numbers: Two numbers that have no common factor other than 1. For example, 17 and 23 are co-prime numbers.