Is 987 a Prime Number?

Numbers can be classified as either prime or composite, based on their number of factors.

A prime number is a natural number greater than 1 that is divisible only by 1 and itself. For example, 3 is a prime number because it has exactly two divisors: 1 and 3.

A composite number is a natural number that has more than two factors. For instance, 6 is a composite number because it is divisible by 1, 2, 3, and 6.

Properties of prime numbers include:

- Prime numbers are always greater than 1

2 is the only even prime number.

- They have exactly two factors: 1 and the number itself.

- Any two distinct prime numbers are co-prime because they share only one common factor: 1.

Since 987 has more than two factors, it is not a prime number.

The defining characteristic of a prime number is that it has only two divisors: 1 and itself. Since 987 has more than two factors, it is not a prime number. Several methods can be used to determine whether a number is prime or composite, including:

- 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 number of divisors:

- If a number has exactly 2 divisors, it is prime.

- If it has more than 2 divisors, it is composite. Let’s check whether 987 is prime or composite.

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

Step 2: Divide 987 by 2, 3, 4, and so on up to the square root of 987.

Step 3: 987 is divisible by 3 (987 ÷ 3 = 329), so 3 is a factor of 987.

Since 987 has more than 2 divisors, it is a composite number.

The divisibility test method involves using a set of rules to check if a number is divisible by another number without a remainder. Here are some tests:

Divisibility by 2: 987 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits is 24 (9 + 8 + 7 = 24), which is divisible by 3. Hence, 987 is divisible by 3.

Divisibility by 5: The last digit is 7, so 987 is not divisible by 5.

Divisibility by 7: Double the last digit (7 × 2 = 14), subtract it from the rest of the number (98 - 14 = 84), and since 84 is divisible by 7, 987 is divisible by 7.

Since 987 is divisible by 3 and 7, it has more than two factors and is therefore composite.

A prime number chart is a tool created using the "Sieve of Eratosthenes" method. The steps are:

Step 1: Write numbers from 1 to 1000.

Step 2: Leave 1 uncolored, as it is neither prime nor composite.

Step 3: Mark 2 as prime and cross out all multiples of 2.

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

Step 5: Repeat this process until all numbers have been checked.

987 will not appear in the list of prime numbers generated by this method, confirming that it is composite.

Prime factorization involves breaking down a number into its prime factors and then multiplying them to achieve the original number.

Step 1: Divide 987 by 3 to get 329.

Step 2: 329 is divisible by 7 (329 ÷ 7 = 47), and 47 is a prime number.

Step 3: Therefore, the prime factorization of 987 is 3 × 7 × 47.

• Composite numbers: Natural numbers greater than 1 that have more than two factors. For example, 987 is a composite number because it is divisible by factors other than 1 and itself.
  
   
• Divisibility rules: A set of rules that help determine whether one number is divisible by another without performing full division.
  
   
• Co-prime numbers: Two numbers with no common factors other than 1. For example, 8 and 15 are co-prime.
  
   
• Prime factorization: The process of expressing a number as the product of its prime factors.
  
   
• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.