Is 1105 a Prime Number?

There are two types of numbers, primarily — 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 have 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 1105 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 1105 has more than two factors, it is not a prime number. Several 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 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 1105 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 1105 by 2. It is not divisible by 2, so 2 is not a factor of 1105. Step 3: Divide 1105 by 3. It is not divisible by 3, so 3 is not a factor of 1105. Step 4: Continue checking divisors up to the square root of 1105. Step 5: When we divide 1105 by 5, it is divisible by 5. Since 1105 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. This is called the Divisibility Test Method. - Divisibility by 2: 1105 is an odd number, so it is not divisible by 2. - Divisibility by 3: The sum of the digits in the number 1105 is 7, which is not divisible by 3. - Divisibility by 5: The unit’s place digit is 5. Therefore, 1105 is divisible by 5. - Divisibility by 7: The steps for checking divisibility by 7 show that 1105 is not divisible by 7. - Divisibility by 11: The alternating sum of the digits in 1105 is 5, which is not divisible by 11. Since 1105 is divisible by 5, 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 table format. Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite. Step 3: Mark 2 as a prime number and cross out all the multiples of 2. Step 4: Mark 3 as a prime number and cross out all the multiples of 3. Step 5: Repeat this process until you reach the desired range. Through this process, we will have a list of prime numbers. 1105 is not present in the list of prime numbers, so 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 1105 as 5 × 221. Step 2: In 5 × 221, 221 is a composite number. Further, break down 221 into 13 × 17. Now we get the product consisting of only prime numbers. Hence, the prime factorization of 1105 is 5 × 13 × 17.

Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1105 is a composite number because it is divisible by 1, 5, 13, 17, 65, 85, 221, and itself. Prime numbers: Natural numbers greater than 1 that have only two factors, 1 and the number itself, are called prime numbers. Divisibility rules: A set of rules that help determine whether a number is divisible by another number without performing division. Prime factorization: The process of expressing a number as a product of its prime factors. Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a given limit by iteratively marking the multiples of each prime number starting from 2.