Is 974 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 974 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 974 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 974 is prime or composite.

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

Step 2: Divide 974 by 2. It is divisible by 2, so 2 is a factor of 974.

Step 3: Divide 974 by 3. It is not divisible by 3, so 3 is not a factor of 974.

Step 4: You can simplify checking divisors up to 974 by finding the root value. We then need to only check divisors up to the root value.

Step 5: Continue checking up to this root value.

Since 974 has divisors beyond 1 and itself, 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. Four is an even number, which means that 974 is divisible by 2.

- Divisibility by 3: The sum of the digits in the number 974 is 20. Since 20 is not divisible by 3, 974 is also not divisible by 3.

- Divisibility by 5: The unit’s place digit is 4. Therefore, 974 is not divisible by 5.

- Divisibility by 7: The last digit in 974 is 4. To check divisibility by 7, double the last digit (4 × 2 = 8). Then, subtract it from the rest of the number (97 - 8 = 89). Since 89 is not divisible by 7, 974 is also not divisible by 7.

- Divisibility by 11: In 974, the sum of the digits in odd positions is 13, and the sum of the digits in even positions is 7. The difference is 6, which is not divisible by 11. Therefore, 974 is not divisible by 11. Since 974 is divisible by 2 and other numbers, it has more than two factors.

Therefore, 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 these steps:

Step 1: Write 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. The list includes numbers like 2, 3, 5, 7, 11, etc.

974 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 multiply those factors to obtain the original number.

Step 1: We can write 974 as 2 × 487.

Step 2: In 2 × 487, 487 is a prime number, so no further factorization is needed.

The prime factorization of 974 is 2 × 487.

• 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 a product of its prime factors.
  
   
• Divisibility test: A method to determine if a number can be divided by another number without leaving a remainder.
  
   
• Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to any given limit.
  
   
• Factors: The numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 4 are 1, 2, and 4 because they divide 4 completely.