Is 933 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 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 933 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 933 has more than two factors, it is not a prime number. Few methods are used to distinguish between prime and composite numbers. A few methods are:

• 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 933 is prime or composite. 

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

Step 2: Divide 933 by 3. It is divisible by 3, so 3 is a factor of 933. 

Step 3: Divide 933 by 5. It is not divisible by 5, so 5 is not a factor of 933.

Step 4: You can simplify checking divisors up to 933 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 933 by 3, 7, and 11, it is divisible by 3 and 7.

Since 933 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: 933 is an odd number, so it is not divisible by 2. 

Divisibility by 3: The sum of the digits in the number 933 is 15. Since 15 is divisible by 3, 933 is divisible by 3.

Divisibility by 5: The unit’s place digit is 3. Therefore, 933 is not divisible by 5. 

Divisibility by 7: Double the last digit (3 × 2 = 6), and subtract it from the rest of the number (93 - 6 = 87). Since 87 is divisible by 3, 933 is divisible by 7.

Divisibility by 11: The alternating sum of the digits is 9 - 3 + 3 = 9, which is not divisible by 11.

Since 933 is divisible by 3 and 7, 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 grid, typically up to 100 or more. 

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. 933 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 multiply those factors to obtain the original number. 

Step 1: We can write 933 as 3 × 311. 

Step 2: Both 3 and 311 are prime numbers.

Thus, the prime factorization of 933 is 3 × 311.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 933 is a composite number because it is divisible by 1, 3, 311, and 933.
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 933 is 3 × 311.
   
• Divisibility: A property that determines if one number can be divided by another without leaving a remainder. For example, 933 is divisible by 3.
   
• Odd numbers: Numbers that are not divisible by 2. For example, 933 is an odd number.
   
• Natural numbers: The set of positive integers starting from 1. For example, 933 is a natural number.