Is 349 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.
• Since 349 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 349 has exactly two factors, it is a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 349 is prime or composite.

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

Step 2: We test divisibility starting from 2 up to the square root of 349.

Step 3: 349 is not divisible by any integer other than 1 and 349 itself. Since 349 has exactly 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: 349 is not even, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 349 is 16. Since 16 is not divisible by 3, 349 is not divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5. Therefore, 349 is not divisible by 5.

Divisibility by 7, 11, 13, etc.: Testing divisibility reveals that 349 is not divisible by any of these primes. Since 349 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 these steps.

Step 1: Write numbers in a range, for example, 1 to 400.

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 400.

Since 349 is present in the list of prime numbers, 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 349 is a prime number, it cannot be broken down into other prime factors.

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

• Composite numbers: Natural numbers greater than 1 that have more than two divisors.

• Divisibility rules: Guidelines used to determine whether one number is divisible by another.

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

• Factorization: The process of breaking down a number into its prime factors.