Is 989 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 989 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 989 has more than two factors, it is not a prime number. Several methods are used to distinguish between prime and composite numbers, including:

• 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 989 is prime or composite.

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

Step 2: Divide 989 by 2. It is not divisible by 2, as it is an odd number.

Step 3: Divide 989 by 3. The sum of the digits (9+8+9=26) is not divisible by 3, so 989 is not divisible by 3.

Step 4: Divide 989 by 5. It does not end in 0 or 5, so it is not divisible by 5.

Step 5: Divide 989 by 7. It is divisible by 7 (989 ÷ 7 = 141), so 7 is a factor of 989.

Since 989 has more than 2 divisors (1, 7, 141, and 989), 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: 989 is odd, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits is 26, which is not divisible by 3.

- Divisibility by 5: The unit's place digit is not 0 or 5, so it is not divisible by 5.

- Divisibility by 7: 989 divided by 7 equals 141, with no remainder, so 989 is divisible by 7.

Since 989 is divisible by 7, it has more than two factors and is therefore a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps:

Step 1: Write numbers in a sequence, such as 1 to 1000.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark prime numbers starting from 2, and cross out all their multiples.

Step 4: Repeat this process for the next unmarked number.

Using this process, 989 is not found in the list of prime numbers up to 1000, confirming 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 start dividing 989 by the smallest prime numbers until we reach a prime. 989 = 7 × 141 141 = 3 × 47 Thus, the prime factorization of 989 is 7 × 3 × 47.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 989 is a composite number because it is divisible by 1, 7, 141, and 989.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, 989 = 7 × 3 × 47.
  
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing full division.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
  
   
• Co-prime numbers: Two numbers with no common factors other than 1. For example, 8 and 15 are co-prime.