Is 215 a Prime Number?

Numbers are classified as either prime numbers or composite numbers, based on the number of factors they have. 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 certain properties: - 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 that is 1. Since 215 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 215 has more than two factors, it is not a prime number. Several methods can be used to distinguish between prime and composite numbers. Some of these methods include: - Counting Divisors Method - Divisibility Test - Prime Number Chart - Prime Factorization

The counting divisors method involves counting the number of divisors to determine whether a number is prime or composite. - If there is a total of only 2 divisors, then the number is prime. - If the count is more than 2, then the number is composite. Let’s check whether 215 is prime or composite. Step 1: All numbers are divisible by 1 and itself. Step 2: Divide 215 by 2. It is not divisible by 2, so 2 is not a factor of 215. Step 3: Divide 215 by 3. It is not divisible by 3, so 3 is not a factor of 215. Step 4: Check divisibility up to the square root of 215, which is approximately 14.7. Step 5: Dividing 215 by 5, it is divisible, so 5 is a factor of 215. Since 215 has more than 2 divisors, it is a composite number.

The divisibility test method uses a set of rules to determine whether a number is divisible by another number without leaving a remainder. - Divisibility by 2: 215 ends in 5, which is not even, so 215 is not divisible by 2. - Divisibility by 3: The sum of the digits in 215 is 8. Since 8 is not divisible by 3, 215 is not divisible by 3. - Divisibility by 5: The unit’s place digit is 5. Therefore, 215 is divisible by 5. - Divisibility by 7: Doubling the last digit (5 × 2 = 10) and subtracting from the rest (21 - 10 = 11) shows 11 is not divisible by 7, so 215 is not divisible by 7. - Divisibility by 11: The alternating sum of the digits in 215 is 2 - 1 + 5 = 6, which is not divisible by 11. Since 215 is divisible only by 1, 5, 43, and 215, it has more than two factors. Therefore, it is a composite number.

The prime number chart is a tool created using the method called "The Sieve of Eratosthenes." Here’s how it works: Step 1: Write the numbers from 1 to 100 in a 10x10 grid. 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 its multiples. Step 4: Mark 3 as a prime number and cross out all its multiples. Step 5: Continue this process for each number up to the square root of the largest number in the chart. Through this process, the list of prime numbers up to 100 is obtained. Since 215 is not on this list, we know its factors include numbers greater than 100, making it composite.

Prime factorization is the process of breaking down a number into its prime factors. Step 1: We can write 215 as 5 × 43. Step 2: Both 5 and 43 are prime numbers. Since the factors of 215 are 5 and 43, neither of which is 1 or 215 itself, we confirm that 215 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, 215 is composite because it is divisible by 1, 5, 43, and 215. Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 215 is 5 × 43. Divisibility rules: Guidelines to determine if one number is divisible by another without performing division. Co-prime numbers: Two numbers are co-prime if their greatest common divisor is 1. Sieve of Eratosthenes: A method to find all prime numbers up to a certain number by marking the multiples of each prime starting from 2.