Is 353 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 353 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 353 has exactly two factors, it is a prime number. A few 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 numbers as prime or composite.

• 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 353 is prime or composite.

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

Step 2: Divide 353 by numbers starting from 2 up to its square root.

Step 3: 353 is not divisible by any number other than 1 and itself.

Since 353 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: 353 is not divisible by 2 because it is an odd number.

Divisibility by 3: The sum of the digits in the number 353 is 11. Since 11 is not divisible by 3, 353 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 353 is not divisible by 5.

Divisibility by 7, 11, 13, etc.: Performing similar checks on these numbers shows that 353 is not divisible by any of them.

Since 353 is not divisible by any number other than 1 and 353, 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 up to 400 or more.

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.

353 is present in the list of prime numbers, so 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.

Step 1: Check if 353 can be divided by any prime number starting from the smallest.

Step 2: 353 is not divisible by any prime number other than 1 and itself.

Therefore, 353 itself is a prime number as it cannot be broken down further into other prime factors.

• Prime numbers: Natural numbers greater than 1 that are divisible by only 1 and themselves. For example, 353 is a prime number.

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

• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.

• Divisibility Test: A method used to determine if a number is divisible by another number without performing division.

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