Is 221 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 221 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 221 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 221 is prime or composite. - Step 1: All numbers are divisible by 1 and itself. - Step 2: Divide 221 by 2. It is not divisible by 2, so 2 is not a factor of 221. - Step 3: Divide 221 by 3. It is not divisible by 3, so 3 is not a factor of 221. - Step 4: You can simplify checking divisors up to 221 by finding the square root value. We then need to only check divisors up to the square root value. - Step 5: When we divide 221 by 11, it is divisible by 11. Since 221 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: The number in the ones' place value of 221 is 1. Therefore, 221 is not divisible by 2. - Divisibility by 3: The sum of the digits in the number 221 is 5. Since 5 is not divisible by 3, 221 is also not divisible by 3. - Divisibility by 5: The unit’s place digit is 1. Therefore, 221 is not divisible by 5. - Divisibility by 11: Subtract and add the digits alternately in 221 (2 - 2 + 1 = 1). Since 1 is not divisible by 11, 221 is not divisible by 11 using this rule. However, direct division shows that 221 is divisible by 11. Since 221 is divisible by numbers other than 1 and itself, 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 sequence, such as from 1 to 100 or more. - 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. 221 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. Then multiply those factors to obtain the original number. - Step 1: We can write 221 as 13 × 17. Since both 13 and 17 are prime numbers, the prime factorization shows that 221 is a composite number.

- Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 221 is a composite number because it is divisible by 1, 13, 17, and 221. - Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves. For example, 13 is a prime number. - Divisibility: A number is divisible by another if you divide them and the remainder is zero. For example, 221 is divisible by 13 and 17. - Factors: The numbers that divide another number exactly without leaving a remainder are called factors. For example, the factors of 221 are 1, 13, 17, and 221. - Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 221 is 13 × 17.