Is 929 a Prime Number?

There are two types of numbers, primarily —

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 929 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 929 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, such as: 

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

The counting divisors method involves counting the number of divisors to categorize numbers as prime or composite. Based on the count of the divisors, numbers are categorized:

• 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 929 is prime or composite. 

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

Step 2: Divide 929 by 2. It is not divisible by 2, as it is an odd number. 

Step 3: Divide 929 by 3. The sum of the digits (9+2+9=20) is not divisible by 3, so 929 is not divisible by 3. 

Step 4: Check divisors up to the approximate square root of 929, which is about 30.5.

Step 5: Dividing 929 by 7 gives an integer quotient (132), making 7 a factor of 929.

Since 929 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: 929 is not divisible by 2, as it is an odd number. 

Divisibility by 3: The sum of the digits is 20, which is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 9, so 929 is not divisible by 5. 

Divisibility by 7: Dividing 929 by 7 gives an integer result (132), showing that 929 is divisible by 7.

Divisibility by 11: The difference between the sum of the digits in odd positions (9 + 9 = 18) and even positions (2) is 16, which is not divisible by 11.

Since 929 is divisible by 7, it has more than two factors, making it a composite number.

The prime number chart uses a method called “The Sieve of Eratosthenes.” In this method, we follow the steps below:

Step 1: Write numbers starting from 1.

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 multiples of 2. 

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

Step 5: Continue this process to list primes. Through this process, we can identify prime numbers.

Since 929 is not found in the list of prime numbers, it is a composite number.

Prime factorization is the process of breaking down a number into its prime factors and multiplying them to obtain the original number.

Step 1: We can write 929 as 7 × 133.

Step 2: Break down 133 further, which is 7 × 19. 

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

Hence, the prime factorization of 929 is 7 × 7 × 19.

• Composite Numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 15 is a composite number because it is divisible by 1, 3, 5, and 15.
   
• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 11 is a prime number.
   
• Divisibility rules: A set of rules to determine if a number is divisible by another number without performing division.
   
• Prime factorization: The process of expressing a number as a product of its prime factors.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to any given limit.