Is 789 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 that is 1. As 789 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 789 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. A few methods are: 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 789 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 789 by 2. It is not divisible by 2. Step 3: Divide 789 by 3. The sum of its digits (7 + 8 + 9 = 24) is divisible by 3, so 789 is divisible by 3. Step 4: You can simplify checking divisors up to 789 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 789 by other numbers, it is divisible by 3. Since 789 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: The number 789 is odd, so it is not divisible by 2. Divisibility by 3: The sum of the digits in the number 789 is 24. Since 24 is divisible by 3, 789 is also divisible by 3. Divisibility by 5: The unit’s place digit is 9. Therefore, 789 is not divisible by 5. Divisibility by 7: The last digit in 789 is 9. Double it (9 × 2 = 18) and subtract it from the rest of the number (78 - 18 = 60). Since 60 is divisible by 3, check divisibility further to ensure accuracy. Divisibility by 11: In 789, the difference between the sum of the digits in odd positions (7 + 9 = 16) and the even position (8) is 8. This means 789 is not divisible by 11. Since 789 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 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. 789 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 multiply those factors to obtain the original number. Step 1: We can write 789 as 3 × 263. Step 2: In 3 × 263, 263 is a prime number. Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 789 is 3 × 263.

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 divisible only by 1 and themselves. For example, 5 is a prime number because it is only divisible by 1 and 5. Divisibility rules: Guidelines used to determine whether one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3. Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3. Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. For example, 8 and 15 are co-prime because they have no common factors other than 1.