Is 1379 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 a few key 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 1379 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 1379 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, such as:

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

The method of counting 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 would be prime.

If the count is more than 2, the number is composite.

Let’s check whether 1379 is prime or composite.

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

Step 2: Divide 1379 by 2. It is not divisible by 2, so 2 is not a factor of 1379.

Step 3: Divide 1379 by 3. It is not divisible by 3, so 3 is not a factor of 1379.

Step 4: You can simplify checking divisors up to 1379 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1379 by 11, it is divisible by 11.

Since 1379 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 9, which is odd, so 1379 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 1379 is 20. Since 20 is not divisible by 3, 1379 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 9. Therefore, 1379 is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 1379 is not divisible by 7.

Divisibility by 11: The alternating sum of the digits (1 - 3 + 7 - 9) is -4, which is not divisible by 11, so 1379 is not divisible by 11.

Since 1379 is divisible by 11, 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 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark 2 because it is a prime number and cross out all the multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all the 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.

The list is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. 1379 is not present in the list of prime numbers, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 1379 as 11 × 125.

Step 2: In 11 × 125, 125 is a composite number. Further, break 125 into 5 × 25.

Step 3: Now break 25 into 5 × 5.

Therefore, the prime factorization of 1379 is 11 × 5 × 5 × 5.

• Prime number: A natural number greater than 1 that is divisible only by 1 and itself.
   
• Composite number: A natural number greater than 1 that has more than two distinct positive divisors.
   
• Factor: A number that divides another number exactly without leaving a remainder.
   
• Divisibility Test: A set of rules to determine if one number is divisible by another.
   
• Prime Factorization: The process of decomposing a number into its prime factors.