Is 813 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 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 813 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 813 has more than two factors, it is not a prime number. 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 813 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 813 by 2. It is not divisible by 2, so 2 is not a factor of 813. Step 3: Divide 813 by 3. It is divisible by 3, so 3 is a factor of 813. Step 4: You can simplify checking divisors up to 813 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 813 by 3, it is divisible by 3. Since 813 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 3. Since 3 is not an even number, 813 is not divisible by 2. Divisibility by 3: The sum of the digits in the number 813 is 12. Since 12 is divisible by 3, 813 is also divisible by 3. Divisibility by 5: The unit’s place digit is 3. Therefore, 813 is not divisible by 5. Divisibility by 7: The last digit in 813 is 3. To check divisibility by 7, double the last digit (3 × 2 = 6). Then, subtract it from the rest of the number (81 - 6 = 75). Since 75 is divisible by 7, 813 is also divisible by 7. Since 813 is divisible by 3 and 7, 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 a structured format. 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 all prime numbers up to 1000. Through this process, we will have a list of prime numbers. 813 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 813 as 3 × 271. Step 2: In 3 × 271, 271 is a prime number. Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 813 is 3 × 271.

Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 813 is a composite number because 813 is divisible by 1, 3, 271, and 813. Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 813 is 3 × 271. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer by systematically marking the multiples of each prime number starting from 2. Divisibility rules: Guidelines to determine if one number is divisible by another without performing division. For example, the rule for 3 states that if the sum of a number's digits is divisible by 3, then the number is divisible by 3. Co-prime numbers: Two numbers that have only 1 as their common factor. For instance, 8 and 15 are co-prime.