Is 796 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 796 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 796 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, such as: - 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 796 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 796 by 2. It is divisible by 2, so 2 is a factor of 796. Step 3: Divide 796 by 3. It is not divisible by 3, so 3 is not a factor of 796. Step 4: You can simplify checking divisors of 796 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 796 by 2, 4, and 199, it is divisible by 2 and 199. Since 796 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 6, which is even. Therefore, 796 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 796 is 22. Since 22 is not divisible by 3, 796 is not divisible by 3. - Divisibility by 5: The unit’s place digit is 6. Therefore, 796 is not divisible by 5. - Divisibility by 7: The last digit in 796 is 6. To check divisibility by 7, double the last digit (6 × 2 = 12). Then, subtract it from the rest of the number (79 - 12 = 67). Since 67 is not divisible by 7, 796 is also not divisible by 7. - Divisibility by 11: In 796, the sum of the digits in odd positions (7 + 6 = 13) and the sum of the digits in even positions (9) have a difference of 4. Therefore, 796 is not divisible by 11. Since 796 is divisible only by 2 and other numbers like 199, 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 numbers in a series. 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 for subsequent numbers. Through this process, we will have a list of prime numbers. Since 796 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 multiplying those factors to obtain the original number. Step 1: We can write 796 as 2 × 398. Step 2: In 2 × 398, 398 is a composite number. Further, break 398 into 2 × 199. Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 796 is 2 × 2 × 199.

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. For example, 28 is written as 2 × 2 × 7. Divisibility rules: A set of rules that help determine if one number is divisible by another without performing actual division. Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 8 and 15 are co-prime. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.