Is 787 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 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 787 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 787 has more than two factors, it is not a prime number. 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 787 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 787 by 2. It is not divisible by 2, so 2 is not a factor of 787. Step 3: Divide 787 by 3. It is not divisible by 3, so 3 is not a factor of 787. Step 4: You can simplify checking divisors up to 787 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 787 by 7 and 11, it is divisible by 11. Since 787 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 in the ones' place value is 7, which is an odd number, so 787 is not divisible by 2. Divisibility by 3: The sum of the digits in the number 787 is 22. Since 22 is not divisible by 3, 787 is also not divisible by 3. Divisibility by 5: The unit’s place digit is 7. Therefore, 787 is not divisible by 5. Divisibility by 11: In 787, the difference between the sum of the digits in odd positions (14) and even positions (8) is 6. Since 6 is not divisible by 11, 787 is not divisible by 11. Since 787 is divisible only by 1, 11, 71, and 787, 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. Since 787 is not present in the list of prime numbers, 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 787 as 11 × 71. Step 2: In 11 × 71, both 11 and 71 are prime numbers. Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 787 is 11 × 71.

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 factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 60 is 2 × 2 × 3 × 5. Divisibility: A number is divisible by another if you divide them and the result is a whole number without a remainder. Co-prime numbers: Two numbers are co-prime if their greatest common divisor (GCD) is 1. For instance, 8 and 15 are co-prime. Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.