Is 375 a Prime Number?

There are mainly two types of numbers — 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.
• As 375 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 375 has more than two factors, it is not a prime number. Several methods can be 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 the 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 would be prime. 
• If the count is more than 2, then the number is composite. Let’s check whether 375 is prime or composite. 

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

Step 2: Divide 375 by 2. It is not divisible by 2. -

Step 3: Divide 375 by 3. It is divisible by 3, so 3 is a factor of 375. -

Step 4: You can simplify checking divisors up to 375 by finding the square root value. We then need to only check divisors up to the square root value.

Since 375 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 5. Since 5 is not even, 375 is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 375 is 15. Since 15 is divisible by 3, 375 is also divisible by 3. -

Divisibility by 5: The unit’s place digit is 5.

Therefore, 375 is divisible by 5. Since 375 is divisible by 3 and 5, it has more than two factors. Therefore, 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 marking 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 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.

Since 375 is not present in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number. - Step 1: We can write 375 as 3 × 125. - Step 2: In 3 × 125, 125 is a composite number. Further, break 125 into 5 × 25. - Step 3: Break 25 into 5 × 5. Now we get the product consisting of only prime numbers. Hence, the prime factorization of 375 is 3 × 5 × 5 × 5.

• 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 that have only two factors, 1 and themselves, are called prime numbers. For example, 7 is a prime number because it is divisible only by 1 and 7.

• Divisibility rules: Guidelines that help determine whether one number is divisible by another.

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

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