Is 785 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 785 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 785 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, including: - 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 785 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 785 by 5. It is divisible by 5, so 5 is a factor of 785. Step 3: Divide 785 by 157. It is divisible by 157, so 157 is also a factor of 785. Step 4: You can simplify checking divisors up to 785 by finding the root value. We then need to only check divisors up to the root value. Since 785 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 785 is odd, so it is not divisible by 2. - Divisibility by 3: The sum of the digits in the number 785 is 20. Since 20 is not divisible by 3, 785 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 5. Therefore, 785 is divisible by 5. - Divisibility by 7: The last digit in 785 is 5. To check divisibility by 7, double the last digit (5 × 2 = 10). Then, subtract it from the rest of the number (78 - 10 = 68). Since 68 is not divisible by 7, 785 is also not divisible by 7. - Divisibility by 11: In 785, the difference between the sum of the digits in odd positions (7 + 5) and the sum of the digits in even positions (8) is 4, which is not divisible by 11. Since 785 is divisible by 5 and 157, 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 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 from 1 to 1000. 785 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 785 as 5 × 157. Step 2: Both 5 and 157 are prime numbers. Hence, the prime factorization of 785 is 5 × 157.

- Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 785 is a composite number because it is divisible by 1, 5, 157, and 785. - Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and itself. For example, 5 is a prime number. - Divisibility rules: A set of guidelines that help determine if one number is divisible by another without performing full division. - Prime factorization: The process of breaking down a number into its prime number components. For instance, the prime factorization of 785 is 5 × 157. - 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.