Is 362 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 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 362 has more than two factors, it is not a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 362 has more than two factors, it is not a prime number. 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 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 362 is prime or composite. -

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

Step 2: Divide 362 by 2. It is divisible by 2, so 2 is a factor of 362. 

Step 3: Divide 362 by 3. It is not divisible by 3, so 3 is not a factor of 362. 

Step 4: You can simplify checking divisors up to 362 by finding the square root value. We then need to only check divisors up to that root value. 

Step 5: When we divide 362 by 2, 181, and others in between, it is divisible by 2.

Since 362 has more than 2 divisors, it is a composite 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: The number in the ones' place value is 2, which is even, meaning that 362 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 362 is 11. Since 11 is not divisible by 3, 362 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 2. Therefore, 362 is not divisible by 5. 

Divisibility by 7: Double the last digit (2 × 2 = 4). Subtract it from the rest of the number (36 - 4 = 32). Since 32 is not divisible by 7, 362 is also not divisible by 7. 

Divisibility by 11: The difference between the sum of the digits in odd positions (3 + 2) and the sum of the digits in even positions (6) is 1. Since 1 is not divisible by 11, 362 is not divisible by 11.

Since 362 is divisible only by 1, 2, 181, and 362, it has more than two factors. Therefore, it is a composite 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 in rows. 

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 have crossed all composite numbers. Through this process, we will have a list of prime numbers.

362 is not present in the list of prime numbers, so it is a composite 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: We can write 362 as 2 × 181. 

Step 2: In 2 × 181, both are prime numbers.

Hence, the prime factorization of 362 is 2 × 181.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12. 

• Prime numbers: Numbers greater than 1 with exactly two factors, 1 and itself. For example, 5 is a prime number. 

• Divisibility test: A set of rules to determine if one number is divisible by another without performing division. 

• Sieve of Eratosthenes: A method to find all prime numbers up to a specified integer. 

• Prime factorization: The process of expressing a number as a product of its prime factors.