Is 979 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 979 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 979 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 979 is prime or composite.

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

Step 2: Divide 979 by 2. It is not divisible by 2.

Step 3: Divide 979 by 3. It is not divisible by 3.

Step 4: You can simplify checking divisors up to 979 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 979 by 11, it is divisible by 11.

Since 979 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 979 is odd, so it is not divisible by 2.

- Divisibility by 3: The sum of the digits in 979 is 25. Since 25 is not divisible by 3, 979 is not divisible by 3.

- Divisibility by 5: The unit’s place digit is 9. Therefore, 979 is not divisible by 5.

- Divisibility by 7: Double the last digit (9 x 2 = 18) and subtract it from the rest (97 - 18 = 79). Since 79 is not divisible by 7, 979 is not divisible by 7.

- Divisibility by 11: The alternating sum and difference of the digits are 9 - 7 + 9 = 11, which is divisible by 11. Thus, 979 is divisible by 11.

Since 979 is divisible by 11, it has more than two factors, making it 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 from 1 to 1000 in appropriate 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 have marked and crossed all relevant numbers. Through this process, we can identify prime numbers from 1 to 1000.

979 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 979 as 11 x 89.

Step 2: Both 11 and 89 are prime numbers.

Thus, the prime factorization of 979 is 11 x 89.

• 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 factorization: The process of expressing a number as the product of its prime factors.
  
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing the actual division.
  
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
  
   
• Co-prime numbers: Two numbers that have only 1 as their common factor.