Is 1396 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.

As 1396 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 1396 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 1396 is prime or composite.

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

Step 2: Divide 1396 by 2. It is divisible by 2, so 2 is a factor of 1396.

Step 3: Divide 1396 by 3. It is not divisible by 3, so 3 is not a factor of 1396.

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

Step 5: When we divide 1396 by various numbers, it is divisible by 2, 4, and other numbers. Since 1396 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. It is called the Divisibility Test Method.

Divisibility by 2: The number in the one's place value is 6. Six is an even number, which means that 1396 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1396 is 19. Since 19 is not divisible by 3, 1396 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 6. Therefore, 1396 is not divisible by 5.

Divisibility by 7: Perform the divisibility test for 7. The calculations reveal that 1396 is not divisible by 7.

Divisibility by 11: By applying the divisibility rule for 11, 1396 is found not divisible by 11. Since 1396 is divisible by 2 and other numbers, it has more than two factors. Therefore, it 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 the following steps.

Step 1: Write numbers in a sequence.

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 to mark primes and cross out composites. Through this process, we can observe that 1396 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 and then multiplying those factors to obtain the original number.

Step 1: We can write 1396 as 2 × 698.

Step 2: In 2 × 698, 698 is a composite number. Further, break the 698 into 2 × 349.

Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1396 is 2 × 2 × 349.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime numbers: Numbers greater than 1 that have no divisors other than 1 and themselves. For example, 13 is a prime number.
   
• Divisibility rules: A set of guidelines to determine if one number is divisible by another without performing division.
   
• Prime factorization: Expressing a number as a product of its prime factors. For example, 28 can be expressed as 2 × 2 × 7.
   
• Co-prime numbers: Two numbers that have only 1 as their common factor. For example, 8 and 15 are co-prime.