Is 1029 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 1029 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 1029 has more than two factors, it is not a prime number. A 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 1029 is prime or composite.

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

Step 2: Divide 1029 by 2. It is not divisible by 2.

Step 3: Divide 1029 by 3. It is divisible by 3, so 3 is a factor of 1029.

Since 1029 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: 1029 is not divisible by 2 as it is an odd number. 

Divisibility by 3: The sum of the digits in the number 1029 is 12. Since 12 is divisible by 3, 1029 is divisible by 3. 

Divisibility by 5: The unit’s place digit is not 0 or 5, so 1029 is not divisible by 5. 

Divisibility by 7: Check divisibility rule for 7, 1029 is not divisible by 7. -

Divisibility by 11: The alternating sum of the digits is 0, which is divisible by 11. So, 1029 is divisible by 11.

Since 1029 has more than two factors, 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 sequence. 

Step 2: Identify and mark prime numbers and cross out all multiples of each prime number.

Through this process, we will have a list of prime numbers.

Since 1029 is not in the list of prime numbers, 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 1029 as 3 × 343. 

Step 2: In 3 × 343, 343 is a composite number. Further, break down 343 into 7 × 49. 

Step 3: Now, break down 49 into 7 × 7.

Hence, the prime factorization of 1029 is 3 × 7 × 7 × 7.

• 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 numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. 
  
   
• Divisibility: A property that determines if one number is divisible by another without leaving a remainder. 
  
   
• Prime factorization: Expressing a number as the product of its prime factors. 
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.