Is 689 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 689 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 689 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include: - 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 either 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 689 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 689 by 2. It is not divisible by 2. Step 3: Divide 689 by 3. It is not divisible by 3. Step 4: You can simplify checking divisors up to 689 by finding the approximate square root value. We then need to only check divisors up to the square root value, which is approximately 26. Step 5: Dividing 689 by 13, we find it is divisible, as 689 ÷ 13 = 53. Since 689 has more than 2 divisors (1, 13, 53, 689), 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 9, which is odd, so 689 is not divisible by 2. - Divisibility by 3: The sum of the digits in the number 689 is 23. Since 23 is not divisible by 3, 689 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 9. Therefore, 689 is not divisible by 5. - Divisibility by 7: To check divisibility by 7, we use a method involving doubling and subtracting. 689 is not divisible by 7. - Divisibility by 11: In 689, the alternating sum of the digits (6 - 8 + 9) is 7, which is not divisible by 11. Since 689 is divisible by 13, it has more than two factors, making it 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 100 or more 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 primes and crossed composites. Through this process, we will have a list of prime numbers. 689 is not present in this list of prime numbers up to its square root, 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 689 as 13 × 53. Step 2: Since both 13 and 53 are prime numbers, the prime factorization of 689 is 13 × 53.

- 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: Numbers greater than 1 having no divisors other than 1 and itself. - 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. - Divisibility rules: Set of guidelines to determine whether a number is divisible by another number without performing division. - Sieve of Eratosthenes: An ancient algorithm for finding all prime numbers up to any given limit.