Is 795 a Prime Number?

There are two main categories of numbers — 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 such as: - 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 because they have only one common factor, which is 1. As 795 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 795 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers, such as: - Counting Divisors Method - Divisibility Test - Prime Number Chart - Prime Factorization

In the counting divisors method, we count the number of divisors to categorize numbers as prime or composite. The number would be considered prime if it has only 2 divisors. If the count is more than 2, then the number is composite. Let’s check whether 795 is prime or composite. - Step 1: All numbers are divisible by 1 and themselves. - Step 2: Divide 795 by 3. It is divisible by 3, so 3 is a factor of 795. - Step 3: Divide 795 by 5. It is not divisible by 5, so 5 is not a factor. - Step 4: You can simplify checking divisors by calculating up to the square root value of 795. - Step 5: When we divide 795 by 3, 5, and 9, it is divisible by 3 and 9. Since 795 has more than 2 divisors, it is a composite number.

The divisibility test uses a set of rules to check whether a number is divisible by another number completely. - Divisibility by 3: The sum of the digits in 795 is 21. Since 21 is divisible by 3, 795 is also divisible by 3. - Divisibility by 5: The unit’s place digit is 5. Therefore, 795 is divisible by 5. - Divisibility by 7: Double the last digit (5 × 2 = 10). Subtract it from the rest of the number (79 - 10 = 69). Since 69 is divisible by 7, 795 is also divisible by 7. Since 795 is divisible by 3, 5, and 7, it has more than two factors and is therefore a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow the steps below: - Step 1: Write numbers from 1 to 1000 in rows and columns. - Step 2: Leave 1 without marking or crossing, as it is neither prime nor composite. - Step 3: Mark 2 because it is a prime number and cross out all multiples of 2. - Step 4: Mark 3 because it is a prime number and cross out all multiples of 3. - Step 5: Repeat this process until you complete the table with marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers up to 1000. Since 795 is not present in the list, it is a composite number.

Prime factorization is a process of breaking down a number into its prime factors, then multiplying those factors to obtain the original number. - Step 1: We can write 795 as 3 × 265. - Step 2: In 3 × 265, 265 is a composite number. Further, break the 265 into 5 × 53. - Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 795 is 3 × 5 × 53.

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 numbers: Natural numbers greater than 1 that are only divisible by 1 and themselves. For example, 7 is a prime number. 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. Divisibility rules: A set of rules that help determine whether one number is exactly divisible by another. Prime factorization: The process of breaking down a number into a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.