Is 1214 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 that is 1. As 1214 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 1214 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers. These methods include: - Counting Divisors Method - Divisibility Test - Prime Number Chart - Prime Factorization

The method in which we count the number of divisors to categorize numbers as prime or composite is called the counting divisors method. Based on the count of the divisors, we categorize numbers as either prime or composite. - If there is a total count 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 1214 is prime or composite. Step 1: All numbers are divisible by 1 and themselves. Step 2: Divide 1214 by 2. It is divisible by 2, so 2 is a factor of 1214. Step 3: Divide 1214 by 3. It is not divisible by 3, so 3 is not a factor of 1214. Step 4: You can simplify checking divisors up to 1214 by finding the root value. We then need to only check divisors up to this root value. Step 5: When we divide 1214 by 2, it is divisible, indicating more than two factors. Since 1214 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. This is called the Divisibility Test Method. - Divisibility by 2: The last digit of 1214 is 4, which is even. Therefore, 1214 is divisible by 2. - Divisibility by 3: The sum of the digits in 1214 is 1 + 2 + 1 + 4 = 8. Since 8 is not divisible by 3, 1214 is also not divisible by 3. - Divisibility by 5: The last digit is not 0 or 5, so 1214 is not divisible by 5. - Divisibility by 7, 11, and other primes can be tested similarly. Since 1214 is divisible by 2, it has more than two factors and is therefore a composite number.

The prime number chart is a tool created using a method called “The Sieve of Eratosthenes.” In this method, we follow these steps: Step 1: Write numbers from 1 to 100 (or beyond) 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 multiples of 2. Step 4: Mark 3 because it is a prime number and cross out all multiples of 3. Step 5: Repeat this process to create a list of prime numbers. Through this process, we see that 1214 is not present in the list of prime numbers, confirming it is a composite number.

Prime factorization is a process of breaking down a number into its prime factors and then multiplying those factors to obtain the original number. Step 1: We can write 1214 as 2 × 607. Step 2: In 2 × 607, 607 is checked for primality, which is prime. Hence, the prime factorization of 1214 is 2 × 607.

1. Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 1214 is a composite number because it is divisible by 1, 2, 607, and 1214. 2. Prime numbers: Numbers that have only two factors, 1 and themselves, are called prime numbers. For example, 607 is a prime number. 3. Divisibility rules: A set of rules used to determine if one number is divisible by another without performing division. 4. Prime factorization: The process of breaking down a number into its prime factors. For example, 1214 = 2 × 607. 5. Even numbers: Numbers that are divisible by 2. For example, 1214 is an even number.