Is 1391 a Prime Number?

There are two types of numbers, mostly 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.

Since 1391 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 1391 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some methods include:

• Counting Divisors Method
   
• Divisibility Test
   
• Prime Number Chart
   
• 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 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, then the number is composite. Let’s check whether 1391 is prime or composite.

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

Step 2: Divide 1391 by 2. It is not divisible by 2, so 2 is not a factor of 1391.

Step 3: Divide 1391 by 3. The sum of the digits (1 + 3 + 9 + 1 = 14) is not divisible by 3, so 3 is not a factor.

Step 4: Continue checking divisibility by other prime numbers up to the square root of 1391, which is about 37.

Step 5: When we divide 1391 by 11, it is divisible by 11 (1391 ÷ 11 = 126.4545...). Since 1391 is divisible by a number other than 1 and itself, it is a composite number.

We use a set of rules to check whether a number is divisible by another number completely or not. It is called the Divisibility Test Method.

Divisibility by 2: The number 1391 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits of 1391 is 14, which is not divisible by 3.

Divisibility by 5: The unit’s place digit is 1, so 1391 is not divisible by 5.

Divisibility by 7: Double the last digit (1 × 2 = 2) and subtract from the rest of the number (139 - 2 = 137). Since 137 is not divisible by 7, 1391 is not divisible by 7.

Divisibility by 11: The alternating sum of digits is (1 - 3 + 9 - 1 = 6), which is not divisible by 11. Since 1391 is divisible by 11, it has more than two factors and is a composite number.

The prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers in a range, for instance, 1 to 1000.

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: Continue this process up to the square root of the largest number in the range. 1391 does not appear in the list of prime numbers as it is divisible by 11, indicating it is a composite number.

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

Step 1: We can express 1391 as a product of prime numbers.

Step 2: Divide 1391 by 11, giving 1391 = 11 × 127.

Step 3: Check if 127 is a prime number. 127 is not divisible by any prime number up to its square root (about 11). So, it is a prime number. Hence, the prime factorization of 1391 is 11 × 127.

• 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 greater than 1 that have only two factors, 1 and themselves. For example, 3 is a prime number.
   
• Factors: The numbers that divide another 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.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a certain number.
   
• Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 30 is 2 × 3 × 5.