Is 1392 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 1392 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 1392 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, including:

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

The method in which we count 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 numbers as prime or composite. 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 1392 is prime or composite

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

Step 2: Divide 1392 by 2. It is divisible by 2, so 2 is a factor of 1392.

Step 3: Check divisibility up to the square root of 1392. The square root is approximately 37.3, so we check divisibility by prime numbers up to 37. Since 1392 is divisible by numbers other than 1 and itself, it has more than 2 divisors, making it 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 2, which is even, meaning 1392 is divisible by 2.

Divisibility by 3: The sum of the digits (1 + 3 + 9 + 2 = 15) is divisible by 3, so 1392 is divisible by 3.

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1392 is not divisible by 5.

Divisibility by 7, 11, etc., can be checked similarly, but since 1392 has already been shown to have other divisors, it is not prime. Since 1392 is divisible by numbers other than 1 and itself, it has more than two factors, confirming it is a composite number.

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

Step 1: Write numbers in sequence, here up to a certain range, like 1 to 100.

Step 2: Leave 1 without marking, as it is neither prime nor composite.

Step 3: Mark prime numbers and cross out their multiples. Since 1392 is not present in a list of prime numbers and does not fit the criteria of having only two factors, it is a composite number.

Prime factorization involves breaking down a number into prime factors and then multiplying those factors to obtain the original number.

Step 1: Factor 1392 by dividing by the smallest prime number, 2: 1392 ÷ 2 = 696.

Step 2: Continue factoring by 2: 696 ÷ 2 = 348, then 348 ÷ 2 = 174, then 174 ÷ 2 = 87.

Step 3: 87 is not divisible by 2, so divide by 3: 87 ÷ 3 = 29.

Step 4: 29 is a prime number. Therefore, the prime factorization of 1392 is 2 × 2 × 2 × 2 × 3 × 29.

• 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 itself.
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4.
   
• Divisibility rules: 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.