Is 791 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. Since 791 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 791 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include: - 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 numbers as prime or composite. - 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 791 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 791 by 2. It is not divisible by 2, so 2 is not a factor of 791. Step 3: Divide 791 by 3. It is not divisible by 3, so 3 is not a factor of 791. Step 4: We can simplify checking divisors up to the square root of 791, approximately 28. Step 5: When we divide 791 by 7, it is divisible, making 7 a factor of 791. Since 791 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: 791 is odd, so it is not divisible by 2. - Divisibility by 3: The sum of the digits in 791 is 17. Since 17 is not divisible by 3, neither is 791. - Divisibility by 5: The unit’s place digit is 1, so 791 is not divisible by 5. - Divisibility by 7: When dividing 791 by 7, it results in a whole number, so 791 is divisible by 7. - Divisibility by 11: The alternating sum of the digits of 791 is 9 - 1 + 7 = 15, which is not divisible by 11. Since 791 is divisible by 7, it has more than two factors, making it 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 from 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. Since 791 is not present in this list, it is a composite number.

Prime factorization is a process of breaking down a number into its prime factors. Then multiply those factors to obtain the original number. Step 1: We can write 791 as 7 × 113. Step 2: Both 7 and 113 are prime numbers. Hence, the prime factorization of 791 is 7 × 113, confirming it is not a prime number.

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. 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: Guidelines that help determine if one number is divisible by another without performing division. Prime factorization: The process of expressing a number as the product of its prime factors. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.