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Last updated on May 26th, 2025

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Is 360 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, barcode generation, prime numbers are used. In this topic, we will be discussing whether 360 is a prime number or not.

Is 360 a Prime Number? for Australian Students
Professor Greenline from BrightChamps

Is 360 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 that is 1.
  • As 360 has more than two factors, it is not a prime number.
Professor Greenline from BrightChamps

Why is 360 Not a Prime Number?

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 360 has more than two factors, it is not 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 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 360 is prime or composite.

 

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

 

Step 2: Divide 360 by 2. It is divisible by 2, so 2 is a factor of 360.

 

Step 3: Divide 360 by 3. It is divisible by 3, so 3 is a factor of 360.

 

Step 4: You can simplify checking divisors up to 360 by finding the root value. We then need to only check divisors up to the root value.

 

Step 5: When we divide 360 by 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360, it has many divisors.

 

Since 360 has more than 2 divisors, it is a composite 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: The number in the ones' place value is 0. Zero is an even number, which means that 360 is divisible by 2.

 

Divisibility by 3: The sum of the digits in the number 360 is 9. Since 9 is divisible by 3, 360 is also divisible by 3.

 

Divisibility by 5: The unit’s place digit is 0. Therefore, 360 is divisible by 5.

 

Divisibility by 7: The last digit in 360 is 0. To check divisibility by 7, double the last digit (0 × 2 = 0). Then, subtract it from the rest of the number (36 - 0 = 36). Since 36 is divisible by 7, 360 is also divisible by 7.

 

Divisibility by 11: In 360, the sum of the digits in odd positions is 3, and the sum of the digits in even positions is 6. The difference is 3, which is not divisible by 11.

 

Since 360 is divisible by multiple numbers, it has more than two factors. Therefore, it is a composite 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 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. 360 is not present in the list of prime numbers, so it is a composite 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: We can write 360 as 2 × 180.

 

Step 2: In 2 × 180, 180 is a composite number. Further, break the 180 into 2 × 90.

 

Step 3: Further, break 90 into 2 × 45.

 

Step 4: Further, break 45 into 3 × 15.

 

Step 5: Finally, break 15 into 3 × 5. Step 6: Now we get the product consisting of only prime numbers.

 

Hence, the prime factorization of 360 is 2 × 2 × 2 × 3 × 3 × 5.

Max Pointing Out Common Math Mistakes

Common Mistakes to Avoid When Determining if 360 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.

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 360 a Prime Number?

1.Is 360 a perfect square?

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2.What is the sum of the divisors of 360?

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3.What are the factors of 360?

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4.What are the closest prime numbers to 360?

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5.What is the prime factorization of 360?

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6.How can children in Australia use numbers in everyday life to understand Is 360 a Prime Number??

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7.What are some fun ways kids in Australia can practice Is 360 a Prime Number? with numbers?

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8.What role do numbers and Is 360 a Prime Number? play in helping children in Australia develop problem-solving skills?

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9.How can families in Australia create number-rich environments to improve Is 360 a Prime Number? skills?

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Professor Greenline from BrightChamps

Important Glossaries for "Is 360 a Prime Number"

  • Prime number: A natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 7 is a prime number.

 

  • Composite number: A natural number greater than 1 that is not prime, meaning it has more than two distinct positive divisors. For example, 8 is a composite number because it is divisible by 1, 2, 4, and 8.

 

  • Divisibility: A number is divisible by another if you divide the first number by the second and get a whole number with no remainder. For example, 10 is divisible by 5.

 

  • Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7.

 

  • Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer. It systematically eliminates the multiples of each prime starting from 2.
Professor Greenline from BrightChamps

About BrightChamps in Australia

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 Australia grasp important math skills, like today’s focus on the Is 360 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 Luna Park Sydney, keeping track of scores at a local cricket 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 Australia learn in many different ways, we tailor our approach to fit each child’s unique style. From the vibrant streets of Sydney to the stunning beaches of the Gold Coast, BrightChamps brings math to life, making it relatable and exciting throughout Australia. 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

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: She loves to read number jokes and games.

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