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Last updated on May 26th, 2025

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Is 353 a Prime Number?

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The numbers that have only two factors, which are 1 and itself, are called prime numbers. For encryption, computer algorithms, and barcode generation, prime numbers are used. In this topic, we will be discussing whether 353 is a prime number or not.

Is 353 a Prime Number? for Vietnamese Students
Professor Greenline from BrightChamps

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.
Professor Greenline from BrightChamps

Why is 353 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
Professor Greenline from BrightChamps

Using the Counting Divisors Method

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.

Professor Greenline from BrightChamps

Using the Divisibility Test Method

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.

Professor Greenline from BrightChamps

Using Prime Number Chart

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.

Professor Greenline from BrightChamps

Using the Prime Factorization Method

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.

Max Pointing Out Common Math Mistakes

Common Mistakes to Avoid When Determining if 353 is a Prime Number

Children might have some misconceptions about prime numbers when they are learning about them. Here are some mistakes that might be made by children.

Mistake 1

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Assuming That All Odd Numbers Are Prime

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Solution: Children have an assumption that all odd numbers are prime numbers. They should be taught that except for 2, most prime numbers are odd, but not all odd numbers are prime. For example, 15 is an odd number, but it has more than two factors, which makes it a composite number.

Ray Thinking Deeply About Math Problems

FAQ on is 353 a Prime Number?

1.Is 353 a perfect square?

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2.What is the sum of the divisors of 353?

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3.What are the factors of 353?

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4.What are the closest prime numbers to 353?

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5.What is the prime factorization of 353?

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6.How can children in Vietnam use numbers in everyday life to understand Is 353 a Prime Number??

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7.What are some fun ways kids in Vietnam can practice Is 353 a Prime Number? with numbers?

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8.What role do numbers and Is 353 a Prime Number? play in helping children in Vietnam develop problem-solving skills?

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9.How can families in Vietnam create number-rich environments to improve Is 353 a Prime Number? skills?

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Professor Greenline from BrightChamps

Important Glossaries for "Is 353 a Prime Number"

  • 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.
Professor Greenline from BrightChamps

About BrightChamps in Vietnam

At BrightChamps, we know numbers are more than just digits—it’s a way to open doors to countless opportunities! Our mission is to help kids all across the Vietnam grasp important math skills, like today’s focus on the Is 353 a Prime Number?with a special focus on understanding prime numbers—in a way that’s lively, enjoyable, and easy to follow. Whether your child is figuring out how fast a roller coaster speeds through Suoi Tien Theme Park, keeping track of scores at a local football match, or managing their allowance to buy the latest gadgets, mastering numbers gives them the confidence they need for everyday challenges. Our interactive lessons make learning both simple and fun. Because kids in the Vietnam learn in many different ways, we tailor our approach to fit each child’s unique style. From the vibrant streets of Ho Chi Minh City to the scenic beauty of Ha Long Bay, BrightChamps brings math to life, making it relatable and exciting throughout Vietnam. Let’s make prime numbers a fun part of every child’s math journey!
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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

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Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

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