Is 658 a Prime Number?

There are two main types of numbers — 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: - 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 658 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 658 has more than two factors, it is not a prime number. Several 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 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 658 is prime or composite. - Step 1: All numbers are divisible by 1 and itself. - Step 2: Divide 658 by 2. It is divisible by 2, so 2 is a factor of 658. - Step 3: Divide 658 by 3. It is not divisible by 3, so 3 is not a factor of 658. - Step 4: You can simplify checking divisors up to 658 by finding the root value. We then need to only check divisors up to the root value. Since 658 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 8. Since 8 is an even number, 658 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 658 is 19. Since 19 is not divisible by 3, 658 is not divisible by 3. - Divisibility by 5: The unit’s place digit is 8. Therefore, 658 is not divisible by 5. Since 658 is divisible by 2, 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 658 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 prime factors. Then multiply those factors to obtain the original number. - Step 1: We can write 658 as 2 × 329. - Step 2: In 2 × 329, 329 is a composite number. Further, break the 329 into 7 × 47. Now we get the product consisting of only prime numbers. Hence, the prime factorization of 658 is 2 × 7 × 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 factorization: A method of expressing a number as a product of its prime factors. 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. Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.