Is 372 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 have specific 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 numbers because they have only one common factor, which is 1.
• As 372 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 372 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, including: -

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 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 is prime.
• If the count is more than 2, then the number is composite. Let’s check whether 372 is prime or composite: -

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

Step 2: Divide 372 by 2. It is divisible by 2, so 2 is a factor of 372. 

Step 3: Divide 372 by 3. It is divisible by 3, so 3 is a factor of 372. 

Step 4: You can simplify checking divisors up to 372 by finding the square root value. We then need to check divisors up to the root value.

Since 372 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. This is called the Divisibility Test Method. -

Divisibility by 2: The number in the ones' place value is 2, which is an even number, meaning that 372 is divisible by 2. -

Divisibility by 3: The sum of the digits in the number 372 is 12. Since 12 is divisible by 3, 372 is also divisible by 3. -

Divisibility by 5: The unit’s place digit is 2. Therefore, 372 is not divisible by 5. -

Divisibility by 7: Remove the last digit (2), double it (4), subtract it from the remaining leading number (37 - 4 = 33), and since 33 is not divisible by 7, 372 is also not divisible by 7. -

Divisibility by 11: The alternating sum of digits (3 - 7 + 2 = -2) is not divisible by 11.

Since 372 is divisible by more than two numbers, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps: -

Step 1: Write numbers from 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 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 you have marked all prime numbers up to 100. Through this process, we will have a list of prime numbers from 1 to 100.

Since 372 is not in the list of prime numbers, it is a composite number.

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 372 as 2 × 186. 

Step 2: In 2 × 186, 186 is a composite number. Further, break 186 into 2 × 93. 

Step 3: Now, break 93 into 3 × 31. 

Step 4: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 372 is 2 × 2 × 3 × 31.

• 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. 

• Prime numbers: Natural numbers greater than 1 with no divisors other than 1 and itself.

• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division. 

• Prime factorization: The expression of a number as a product of its prime factors. For instance, the prime factorization of 18 is 2 × 3 × 3.

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