Is 923 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 that is 1.
   
• As 923 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 923 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 923 is prime or composite.

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

Step 2: Divide 923 by 2. It is not divisible by 2, so 2 is not a factor of 923.

Step 3: Divide 923 by 3. The sum of the digits (9 + 2 + 3 = 14) is not divisible by 3, so 3 is not a factor of 923.

Step 4: You can simplify checking divisors up to 923 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 923 by 13, it is divisible by 13.

Since 923 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 ones' place value is 3, which is odd, meaning that 923 is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 923 is 14. Since 14 is not divisible by 3, 923 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 3. Therefore, 923 is not divisible by 5.

Divisibility by 7: The last digit in 923 is 3. To check divisibility by 7, double the last digit (3 × 2 = 6). Then, subtract it from the rest of the number (92 - 6 = 86). Since 86 is not divisible by 7, 923 is also not divisible by 7.

Divisibility by 11: In 923, the alternating sums of the digits are 9 - 2 + 3 = 10. Since 10 is not divisible by 11, 923 is not divisible by 11.

Since 923 is divisible by 13, 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 1 to 1000 in rows and columns.

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 from 1 to 1000. The list does not include 923, 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 923 as 13 × 71.

Step 2: Both 13 and 71 are prime numbers.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 923 is 13 × 71.

• 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 expressing a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Factors: The numbers that divide the 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.