Is 1102 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, such as: - 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 1102 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 1102 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers, such as: - 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 1102 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 1102 by 2. It is divisible by 2, so 2 is a factor of 1102. Step 3: Divide 1102 by 3. It is not divisible by 3, so 3 is not a factor of 1102. Step 4: You can simplify checking divisors up to 1102 by finding the square root value. We then need to only check divisors up to the square root value. Step 5: When we divide 1102 by 2, 11, and 101, it is divisible by 2, 11, and 101. Since 1102 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 2. Since 2 is an even number, 1102 is divisible by 2. - Divisibility by 3: The sum of the digits in the number 1102 is 4. Since 4 is not divisible by 3, 1102 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 2. Therefore, 1102 is not divisible by 5. - Divisibility by 7: Use the rule for divisibility by 7 to check 1102; it is not divisible by 7. - Divisibility by 11: Use the alternating sum rule for 1102; it is divisible by 11. Since 1102 is divisible by factors other than 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 these steps: Step 1: Write numbers from 1 to 100 in 10 rows and 10 columns. Step 2: Leave 1 unmarked 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 for subsequent numbers until you reach 100. Through this process, we have a list of prime numbers from 1 to 100. Since 1102 is greater than 100, verify using other methods. As we discovered earlier, 1102 is divisible by 2 and 11, confirming it is not prime.

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 1102 as 2 × 551. Step 2: In 2 × 551, 551 is a composite number. Further, break 551 into 11 × 50.1, but simplify using integer factors. Step 3: Correct factorization shows 551 = 11 × 50.1 not accurate; instead, use 11 × 101. Hence, the prime factorization of 1102 is 2 × 11 × 101.

Prime numbers: Natural numbers greater than 1 with only two divisors, 1 and itself. Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. Divisibility rules: Rules that help determine whether a number is divisible by another number without performing division. Prime factorization: The process of expressing a number as the product of its prime factors. Sieve of Eratosthenes: A method for finding all prime numbers up to a certain integer.