Is 921 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, such as:

• 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 921 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 921 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include:

• 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 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 921 is prime or composite.

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

Step 2: Divide 921 by 2. It is not divisible by 2, so 2 is not a factor of 921.

Step 3: Divide 921 by 3. It is divisible by 3, so 3 is a factor of 921.

Step 4: Continue checking divisors up to the square root of 921, which is approximately 30.

Step 5: When we divide 921 by 3, 7, and 11, it is divisible by 3 and 11.

Since 921 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: 921 is not divisible by 2 because it is an odd number. Divisibility by 3: The sum of the digits in 921 is 12. Since 12 is divisible by 3, 921 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 1. Therefore, 921 is not divisible by 5.

Divisibility by 7: For 921, double the last digit (1 × 2 = 2). Subtract it from the rest of the number (92 - 2 = 90). Since 90 is divisible by 7, 921 is also divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd positions and even positions is 0, which is divisible by 11. Therefore, 921 is divisible by 11.

Since 921 is divisible by 3, 7, and 11, 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 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 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 number 100, marking and crossing as necessary.

Through this process, we will have a list of prime numbers from 1 to 100. Since 921 is greater than 100, you can extend the pattern to identify that 921 is not in the list of primes. Thus, 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 921 as 3 × 307.

Step 2: Check if 307 is a prime number. 307 can be broken into 11 × 28, where 28 is not a prime number.

Step 3: Further break down the composite factors until all are prime.

Therefore, the prime factorization of 921 is 3 × 11 × 28.

• Prime Numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself.
   
• Composite Numbers: Natural numbers greater than 1 that are divisible by more than two different numbers.
   
• Divisibility Rules: Guidelines that help determine if one number is divisible by another without performing division.
   
• Prime Factorization: The process of expressing a number as the product of its prime factors.
   
• Factors: Numbers that divide a given number exactly, leaving no remainder.