Is 1332 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 follow a few properties:

• 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 1332 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 1332 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, such as: 

• 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 is prime. 
• If the count is more than 2, then the number is composite.
   

Let’s check whether 1332 is prime or composite.

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

Step 2: Divide 1332 by 2. It is divisible by 2, so 2 is a factor of 1332.

Step 3: Divide 1332 by 3. It is divisible by 3, so 3 is a factor of 1332.

Step 4: Simplify checking divisors up to the square root of 1332.

Step 5: When we divide 1332 by 2, 3, 4, 6, 9, and 37, it is divisible by all these numbers.

Since 1332 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 2. Since 2 is an even number, 1332 is divisible by 2. -

Divisibility by 3: The sum of the digits in 1332 is 9. Since 9 is divisible by 3, 1332 is divisible by 3.

Divisibility by 5: The unit’s place digit is 2. Therefore, 1332 is not divisible by 5.

Divisibility by 7: By applying the rule for 7, we double the last digit (2 × 2 = 4) and subtract it from the rest (133 - 4 = 129). Since 129 is divisible by 7, 1332 is divisible by 7.

Divisibility by 11: The alternating sum of digits (1 - 3 + 3 - 2 = -1) is not divisible by 11, so 1332 is not divisible by 11.

Since 1332 is divisible by 2, 3, and 7, 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 numbers from 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 as a prime number and cross out all the multiples of 2.

Step 4: Mark 3 as a prime number and cross out all the multiples of 3.

Step 5: Repeat this process until the table consists of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers from 1 to 100.

Since 1332 is not in this list, 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 1332 as 2 × 666.

Step 2: In 2 × 666, 666 is a composite number. Further, break 666 into 2 × 333.

Step 3: Break 333 further into 3 × 111.

Step 4: Break 111 into 3 × 37. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 1332 is 2 × 2 × 3 × 3 × 37.

• 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 factorization: The process of breaking down a number into its prime factors.

• Divisibility: The ability of one number to be divided by another without leaving a remainder.

• Sieve of Eratosthenes: A method used to find all prime numbers up to a specified integer.

• Co-prime numbers: Two numbers that have only 1 as their common factor.