Is 357 a Prime Number?
2026-02-28 17:35 Diff
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Last updated on August 5, 2025

The numbers that have only two factors, which are 1 and itself, are called prime numbers. They are essential in various fields such as encryption, computer algorithms, and barcode generation. In this topic, we will be discussing whether 357 is a prime number or not.

Is 357 a Prime Number?

There are two main types of numbers — prime numbers and composite numbers, depending on the number of factors they have. 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 such as: -

  • 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 because they have only one common factor, which is 1.
  • Since 357 has more than two factors, it is not a prime number.

Why is 357 Not a Prime Number?

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 357 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. Some of these methods include: -

  1. Counting Divisors Method 
  2. Divisibility Test 
  3. Prime Number Chart 
  4. Prime Factorization

Using the Counting Divisors Method

The counting divisors method involves counting the number of divisors a number has to categorize it as either prime or composite. -

  • If there is a total count of only 2 divisors, then the number is prime. 
  • If the count is more than 2, then the number is composite. Let’s check whether 357 is prime or composite.

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

Step 2: Divide 357 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 357 by 3. The sum of the digits (3 + 5 + 7 = 15) is divisible by 3, so 357 is divisible by 3.

Step 4: Continue checking divisors up to the square root of 357, approximately 18.9.

Since 357 has more than 2 divisors, it is a composite number.

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Using the Divisibility Test Method

We use a set of rules to check whether a number is completely divisible by another number, known as the Divisibility Test Method. -

Divisibility by 2: 357 is odd, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits (3 + 5 + 7 = 15) is divisible by 3, so 357 is divisible by 3. 

Divisibility by 5: The last digit is 7, so 357 is not divisible by 5. 

Divisibility by 7: Doubling the last digit (7 × 2 = 14) and subtracting from the rest of the number (35 - 14 = 21), 21 is divisible by 7, so 357 is divisible by 7. 

Divisibility by 11: The difference between the sum of the digits in odd positions and even positions is (3 + 7) - 5 = 5, which is not divisible by 11.

Since 357 is divisible by 3 and 7, it has more than two factors and is therefore a composite number.

Using Prime Number Chart

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” This method involves the following steps:

Step 1: Write numbers from 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 unmarked, 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 the table is filled with marked and crossed boxes, except for 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 357 is not in this list, and it has divisors other than 1 and itself, it is a composite number.

Using the Prime Factorization Method

Prime factorization is a process of breaking down a number into its prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 357 as 3 × 119.

Step 2: In 3 × 119, 3 is a prime number. Further, break down 119 into 7 × 17, where both 7 and 17 are primes.

Step 3: The complete prime factorization of 357 is 3 × 7 × 17.

Common Mistakes to Avoid When Determining if 357 is Not 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.

FAQ on is 357 a Prime Number?

1.Is 357 a perfect square?

2.What is the sum of the divisors of 357?

The sum of the divisors of 357 is 576.

3.What are the factors of 357?

357 is divisible by 1, 3, 7, 17, 21, 51, 119, and 357, making these numbers its factors.

4.What are the closest prime numbers to 357?

353 and 359 are the closest prime numbers to 357.

5.What is the prime factorization of 357?

The prime factorization of 357 is 3 × 7 × 17.

Important Glossaries for "Is 357 a Prime Number"

  • 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 it is divisible by 1, 2, 3, 4, 6, and 12. 
  • Divisibility rules: Guidelines used to determine if one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3. 
  • Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7. 
  • Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1. For example, 8 and 15 are co-prime. 
  • Natural numbers: A set of positive integers starting from 1 and increasing without bound.

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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.

Fun Fact

: She loves to read number jokes and games.