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Last updated on April 29th, 2025
The numbers that have only two factors, which are 1 and itself, are called prime numbers. Prime numbers are essential in fields such as encryption, computer algorithms, and barcode generation. In this topic, we will be discussing whether 1380 is a prime number or not.
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:
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:
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.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.