Is 849 a Prime Number?

There are two main types of numbers based on the number of factors: prime numbers and composite numbers. 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 have 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 numbers because they have only one common factor, which is 1. Since 849 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 849 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 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 849 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 849 by 2. It is not divisible by 2, so 2 is not a factor of 849. Step 3: Divide 849 by 3. The sum of the digits (8 + 4 + 9 = 21) is divisible by 3, so 849 is divisible by 3. Step 4: You can simplify checking divisors up to 849 by finding the root value. We then need to only check divisors up to the root value. Since 849 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. This is called the Divisibility Test Method. - Divisibility by 2: The number is odd, so it is not divisible by 2. - Divisibility by 3: The sum of the digits in the number 849 is 21. Since 21 is divisible by 3, 849 is also divisible by 3. - Divisibility by 5: The unit’s place digit is not 0 or 5, so it is not divisible by 5. - Divisibility by 7: Double the last digit (9 × 2 = 18). Subtract it from the rest of the number (84 - 18 = 66). Since 66 is divisible by 3 but not 7, 849 is not divisible by 7. - Divisibility by 11: The difference between the sum of the digits in odd positions (8 + 9 = 17) and even positions (4) is 13, which is not divisible by 11. Since 849 is divisible by 3, 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 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 for each following prime until you reach the table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers. 849 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 multiplying those factors to obtain the original number. Step 1: We can write 849 as 3 × 283. Step 2: In 3 × 283, 283 is a composite number. Further factor it if possible. Step 3: The product consists of only prime numbers. Hence, the prime factorization of 849 is 3 × 283.

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: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Factors: The numbers that divide a 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: The ability for one number to be divided by another without leaving a remainder. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.