Is 371 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 371 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 371 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. A few methods are:

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 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 371 is prime or composite.

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

Step 2: Divide 371 by 2. It is not divisible by 2, so 2 is not a factor of 371.

Step 3: Divide 371 by 3. It is not divisible by 3, so 3 is not a factor of 371.

Step 4: You can simplify checking divisors up to 371 by finding the root value, which is approximately 19.2. We then need to only check divisors up to this root value.

Step 5: When we divide 371 by 7, it is divisible, so 7 is a factor of 371.

Since 371 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 is 1. Since 1 is odd, 371 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 371 is 11. Since 11 is not divisible by 3, 371 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 371 is not divisible by 5.

Divisibility by 7: Using the rule for 7, we find that 371 is divisible by 7.

Since 371 is divisible by 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 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. 371 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 371 as 7 × 53.

Step 2: Both 7 and 53 are prime numbers.

Step 3: The product consists of only prime numbers.

Hence, the prime factorization of 371 is 7 × 53.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

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

• Divisibility test: A set of rules to determine if one number is divisible by another without performing division.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

• Co-prime numbers: Two numbers that have no common factor other than 1.