Is 1125 a Prime Number?

Numbers can be classified into two types Prime numbers and composite numbers, depending on their 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 have a few properties: 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 1125 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 1125 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers. A few methods include:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• Prime Factorization

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. If there are only 2 divisors, then the number is prime. If the count is more than 2, then the number is composite. Let’s check whether 1125 is prime or composite.

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

Step 2: Divide 1125 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 1125 by 3. The sum of the digits (1 + 1 + 2 + 5 = 9) is divisible by 3, so 1125 is divisible by 3.

Step 4: Continue checking divisors up to the square root of 1125 (approximately 33.5). Since 1125 has more than 2 divisors, it is a composite number.

A set of rules is used to check whether a number is divisible by another number completely, known as the Divisibility Test Method.

Divisibility by 2: 1125 is not divisible by 2 as it is odd.

Divisibility by 3: The sum of the digits is 9, which is divisible by 3, so 1125 is divisible by 3.

Divisibility by 5: The unit’s place digit is 5. Therefore, 1125 is divisible by 5.

Divisibility by 7, 11, etc., can be tested similarly. Since 1125 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 the “Sieve of Eratosthenes” method. In this method, we follow the following steps:

Step 1: Write numbers up to a certain limit, say 1 to 100.

Step 2: Leave 1 unmarked, as it is neither prime nor composite.

Step 3: Mark the smallest unmarked number as a prime and cross out its multiples.

Step 4: Repeat the process. Through this process, we identify the prime numbers. 1125 is not on the list of prime numbers, confirming it is composite.

Prime factorization is the process of breaking down a number into its prime factors. Multiply these factors to obtain the original number.

Step 1: We can write 1125 as 3 × 375.

Step 2: Break down 375 as 3 × 125.

Step 3: Further break down 125 as 5 × 25.

Step 4: Finally, break down 25 as 5 × 5. This results in the prime factorization: 3 × 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, 1125 is a composite number because it is divisible by multiple numbers.
   
• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 7 is a prime number.
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, 1, 3, and 5 are factors of 15.
   
• Divisibility rules: Guidelines to determine if one number is divisible by another. These rules help identify factors quickly.
   
• Prime factorization: Breaking down a composite number into a product of prime numbers. For example, the prime factorization of 30 is 2 × 3 × 5.