Is 373 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.
• Since 373 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 373 has exactly two factors, it is a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 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 is prime.
• If the count is more than 2, then the number is composite.

Let’s check whether 373 is prime or composite.

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

Step 2: Divide 373 by 2. It is not divisible by 2.

Step 3: Divide 373 by 3. It is not divisible by 3.

Step 4: You can simplify checking divisors up to 373 by finding the root value. We then need to only check divisors up to the root value.

Since 373 has only 2 divisors, it is a prime 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: 373 is an odd number, so it is not divisible by 2. -

Divisibility by 3: The sum of the digits in 373 is 13, which is not divisible by 3. - Divisibility by 5: The unit’s place digit is 3, so 373 is not divisible by 5. 

Divisibility by 7: There is no simple rule for 373, but checking directly shows it is not divisible by 7. 

Divisibility by 11: The alternating sum of digits is 7, which is not divisible by 11.

Since 373 is not divisible by any of these numbers, it remains with only 1 and itself as divisors, confirming it is a prime number.

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

Step 1: Write numbers from 1 to 1000 in a systematic format.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark 2 as a prime number and cross out all multiples of 2.

Step 4: Continue with 3, marking it as prime and crossing out its multiples.

Step 5: Repeat this process, marking subsequent primes and crossing out their multiples. Through this process, we will have a list of prime numbers. 373 is not crossed out, so it is a prime 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: Attempt to divide 373 by the smallest prime number, 2. It is not divisible.

Step 2: Attempt division by 3. It is not divisible.

Step 3: Continue with the next primes up to approximately the square root of 373.

Since no prime numbers divide 373 except 1 and itself, prime factorization confirms that 373 is a prime number.

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

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. 

• Divisibility rules: Rules to determine if a number is divisible by another number without performing division. 

• Prime factorization: The process of determining which prime numbers multiply into the original number. 

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.