Is 984 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, which is 1

As 984 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 984 has more than two factors, it is not a prime number. Several methods can be 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 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 984 is prime or composite.

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

Step 2: Divide 984 by 2. It is divisible by 2, so 2 is a factor of 984.

Step 3: Divide 984 by 3. It is divisible by 3, so 3 is a factor of 984.

Step 4: You can simplify checking divisors up to the square root of 984. We then need to only check divisors up to this root value.

Since 984 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 4. Since 4 is an even number, 984 is divisible by 2

- Divisibility by 3: The sum of the digits in the number 984 is 21. Since 21 is divisible by 3, 984 is also divisible by 3

- Divisibility by 5: The unit’s place digit is 4. Therefore, 984 is not divisible by 5.

- Divisibility by 7: A divisibility test for 7 shows that 984 is divisible by 7.

- Divisibility by 11: In 984, the difference between the sum of the digits in odd positions (9 + 4) and the sum of the digits in even positions (8) is 5. This means that 984 is not divisible by 11. Since 984 is divisible by multiple numbers other than 1 and itself, it has more than two factors.

Therefore, it is a composite number.

A prime number chart is a tool created by using a method called “The Sieve of Eratosthenes.” In this method, the following steps are used:

Step 1: Write numbers from 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.

984 is not present in the list of prime numbers, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 984 as 2 × 492.

Step 2: In 2 × 492, 492 is a composite number. Further break down 492 into 2 × 246.

Step 3: Continue breaking down until obtaining only prime numbers.

The prime factorization of 984 is 2 × 2 × 2 × 3 × 41.

Since it consists of more than two prime factors, 984 is a composite number.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
  
   
• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 5 is a prime number because it is divisible only by 1 and itself.
  
   
• Divisibility: A property that determines if a number can be divided by another number without leaving a remainder.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
  
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.