Is 846 a Prime Number?

There are two main types of numbers—prime numbers and composite numbers—depending on the number of factors they have. A prime number is a natural number that is divisible only by 1 and itself. For instance, 3 is a prime number because it is divisible only 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 846 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 846 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 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 is prime. - If the count is more than 2, then the number is composite. Let’s check whether 846 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 846 by 2. It is divisible by 2, so 2 is a factor of 846. Step 3: Divide 846 by 3. It is divisible by 3, so 3 is a factor of 846. Step 4: Simplify checking divisors up to 846 by finding the approximate square root value. We then need to only check divisors up to the root value. Since 846 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 in the ones' place value is 6, an even number, which means that 846 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 846 is 18. Since 18 is divisible by 3, 846 is also divisible by 3. - Divisibility by 5: The unit’s place digit is 6. Therefore, 846 is not divisible by 5. - Divisibility by 7: To check divisibility by 7, double the last digit (6 × 2 = 12) and subtract it from the rest of the number (84 - 12 = 72). Since 72 is divisible by 7, 846 is also divisible by 7. - Divisibility by 11: The difference between the sum of the digits in odd positions and even positions is 0 (8 + 6 - 4 = 10 - 10 = 0). Since 0 is divisible by 11, 846 is divisible by 11. Since 846 is divisible by more than two numbers, 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 these steps: Step 1: Write numbers from 1 to 1000 in rows and columns. Step 2: Leave 1 without marking, 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. Through this process, we obtain a list of prime numbers. Since 846 is not in the list of prime numbers, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number. Step 1: We can write 846 as 2 × 423. Step 2: In 2 × 423, 423 is a composite number. Further, break 423 into 3 × 141. Step 3: Break 141 into 3 × 47, where 47 is a prime number. Thus, the prime factorization of 846 is 2 × 3 × 3 × 47.

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 it is divisible by 1, 2, 3, 4, 6, and 12. Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 7 is a prime number as it is divisible only by 1 and 7. Divisibility rules: Guidelines used to determine if one number is divisible by another without performing division. Prime factorization: The expression of a number as a product of its prime factors. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.