Is 688 a Prime Number?

There are mainly two 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, 7 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, 12 is divisible by 1, 2, 3, 4, 6, and 12, 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 because they have only one common factor, which is 1. As 688 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 688 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. Some 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 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 688 is prime or composite. Step 1: All numbers are divisible by 1 and themselves. Step 2: Divide 688 by 2. It is divisible by 2, so 2 is a factor of 688. Step 3: Divide 688 by 3. It is not divisible by 3, so 3 is not a factor of 688. Step 4: You can simplify checking divisors up to 688 by finding the square root value. We then need to only check divisors up to the square root value. Step 5: When we divide 688 by 2, 4, 8, etc., it is divisible by 2, 4, and 8. Since 688 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, which is an even number. Therefore, 688 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 688 is 22. Since 22 is not divisible by 3, 688 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 8, which means 688 is not divisible by 5. - Divisibility by 7: Use the rule of doubling the last digit (8 × 2 = 16) and subtracting it from the rest (68 - 16 = 52). Since 52 is not divisible by 7, 688 is not divisible by 7. - Divisibility by 11: The alternating sum of the digits of 688 (6 - 8 + 8 = 6) is not divisible by 11, so 688 is not divisible by 11. Since 688 is divisible by more than two numbers, it is a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps: Step 1: Write numbers from 1 to 100 in 10 rows and 10 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 100. The list includes numbers like 2, 3, 5, 7, 11, 13, 17, etc. Since 688 is not in this list, it is a composite number.

Prime factorization is a process of breaking down a number into prime factors and then multiplying those factors to obtain the original number. Step 1: We can write 688 as 2 × 344. Step 2: In 2 × 344, 344 is a composite number. Further, break 344 into 2 × 172. Step 3: Further break down 172 into 2 × 86, and 86 into 2 × 43. Step 4: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 688 is 2 × 2 × 2 × 2 × 43.

- Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 688 is a composite number because it has multiple divisors. - Prime numbers: A number greater than 1 with no divisors other than 1 and itself. For example, 7 is a prime number. - Factors: Numbers that divide another number exactly without leaving a remainder. For example, 1, 2, 4, and 8 are factors of 8. - Divisibility test: A set of rules to determine if one number is divisible by another without performing division. - Prime factorization: Expressing a number as the product of its prime factors. For example, the prime factorization of 688 is 2 × 2 × 2 × 2 × 43.