Is 824 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 824 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 824 has more than two factors, it is not a prime number. A few methods are 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 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 824 is prime or composite.

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

Step 2: Divide 824 by 2. It is divisible by 2, so 2 is a factor of 824.

Step 3: You can simplify checking divisors by finding the square root value, which is approximately 28.7. We then need to only check divisors up to this value.

Step 4: When we divide 824 by 2, 4, 8, 103, and 206, it is divisible by all these numbers.

Since 824 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. Four is an even number, which means that 824 is divisible by 2.

Divisibility by 4: The last two digits of 824 are 24, which is divisible by 4, so 824 is divisible by 4. 

Divisibility by 8: Half of 24 is 12, which is divisible by 4, so 824 is divisible by 8. 

Divisibility by 3: The sum of the digits in the number 824 is 14, which is not divisible by 3, so 824 is not divisible by 3. 

Divisibility by 5: The unit’s place digit is 4, so 824 is not divisible by 5. Since 824 is divisible by 2, 4, and 8, 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 the following 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.

Since 824 is not present in the list of prime numbers, 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 824 as 2 × 412.

Step 2: In 2 × 412, 412 is a composite number. Further, break 412 into 2 × 206.

Step 3: Finally, break 206 into 2 × 103.

Step 4: Now, we get the product consisting of only prime numbers.

Hence, the prime factorization of 824 is 2 × 2 × 2 × 103.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 824 is a composite number because it is divisible by 1, 2, 4, 8, 103, 206, 412, and 824. 

• Prime factorization: The process of expressing a number as a product of prime numbers. For example, the prime factorization of 824 is 2 × 2 × 2 × 103. 

• Divisibility rules: A set of rules to determine if one number is divisible by another without performing division. For example, a number is divisible by 2 if its last digit is even. 

• Sieve of Eratosthenes: An ancient algorithm used to determine all primes up to a certain number. It involves marking the multiples of each prime number starting from 2. 

• Factors: Numbers that divide the number exactly without leaving a remainder are called factors. For example, the factors of 824 are 1, 2, 4, 8, 103, 206, 412, and 824.