Is 1168 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 1168 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 1168 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 1168 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 1168 by 2. It is divisible by 2, so 2 is a factor of 1168. Step 3: Divide 1168 by 3. It is not divisible by 3, so 3 is not a factor of 1168. Step 4: You can simplify checking divisors up to 1168 by finding the root value. We then need to only check divisors up to the root value. Step 5: When we divide 1168 by 2, 4, and 8, it is divisible by 2, 4, and 8. Since 1168 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, 1168 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 1168 is 16. Since 16 is not divisible by 3, 1168 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 8. Therefore, 1168 is not divisible by 5. - Divisibility by 7: The last digit in 1168 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then, subtract it from the rest of the number (116 - 16 = 100). Since 100 is not divisible by 7, 1168 is also not divisible by 7. - Divisibility by 11: In 1168, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 6. This would mean that 1168 is not divisible by 11. Since 1168 is divisible by more numbers than just 1 and itself, 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 numbers in a range, for example, 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 in the range we selected. Since 1168 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 1168 as 2 × 584. Step 2: In 2 × 584, 584 is a composite number. Further, break the 584 into 2 × 292. Step 3: Now break 292 into 2 × 146. Step 4: Finally, break 146 into 2 × 73. Step 5: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1168 is 2 × 2 × 2 × 2 × 73.

- Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 20 is a composite number because 20 is divisible by 1, 2, 4, 5, 10, and 20. - Divisibility rules: Guidelines used to determine if a number is divisible by another without performing the division. For example, a number is divisible by 2 if its last digit is even. - Prime factorization: The process of breaking down a composite number into the product of its prime factors. For example, the prime factorization of 30 is 2 × 3 × 5. - Sieve of Eratosthenes: A simple, ancient algorithm to find all prime numbers up to a specified integer. - 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.