Is 1380 a Prime Number?

There are two main 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 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 1380 has more than two factors, it is not a prime number.
  
  

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1380 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. A few methods are:
 

• 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. Based on the count of the divisors, we categorize 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 1380 is prime or composite.

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

Step 2: Divide 1380 by 2. It is divisible by 2, so 2 is a factor of 1380.

Step 3: Divide 1380 by 3. The sum of the digits (1 + 3 + 8 + 0 = 12) is divisible by 3, so 3 is a factor.

Step 4: You can simplify checking divisors up to 1380 by finding the square root value. We need to only check divisors up to this value.

Step 5: Continue checking divisibility with other numbers such as 5, 7, etc.

Since 1380 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 is 0, which is even, so 1380 is divisible by 2.

Divisibility by 3: The sum of the digits is 12, which is divisible by 3, so 1380 is divisible by 3.

Divisibility by 5: The unit’s place digit is 0, so 1380 is divisible by 5.

Divisibility by 10: The last digit is 0, so 1380 is divisible by 10.

Since 1380 is divisible by multiple numbers, it has more than two factors, confirming it as a composite number.

A 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 a grid.

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

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

Step 4: Mark 3 as a prime number and cross out all its multiples.

Step 5: Repeat this process up to the square root of the largest number in the chart. Through this process, we will have a list of prime numbers.

Since 1380 is not 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: Start with 1380, which can be divided by 2 to get 690.

Step 2: Divide 690 by 2 to get 345.

Step 3: Divide 345 by 3 to get 115.

Step 4: Divide 115 by 5 to get 23, which is a prime number.

Thus, the prime factorization of 1380 is 2 × 2 × 3 × 5 × 23.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 14 is a composite number because it is divisible by 1, 2, 7, and 14.
   
• Prime factorization: The process of expressing a number as the product of its prime numbers. For example, the prime factorization of 18 is 2 × 3 × 3.


• Divisibility rules: Rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 5 if it ends in 0 or 5.
   
• Sieve of Eratosthenes: An ancient algorithm to find all prime numbers up to a specified integer by iteratively marking the multiples of each prime number starting from 2.


• Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1. For example, 9 and 28 are co-prime because their GCD is 1.