Is 212 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 212 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 212 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 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 212 is prime or composite. Step 1: All numbers are divisible by 1 and themselves. Step 2: Divide 212 by 2. It is divisible by 2, so 2 is a factor of 212. Step 3: Divide 212 by 3. It is not divisible by 3, so 3 is not a factor of 212. Step 4: You can simplify checking divisors up to 212 by finding the square root value. We then need to only check divisors up to the root value. Step 5: When we divide 212 by 2, 4, and 6, it is divisible by 2 and 4. Since 212 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 is 2. Two is an even number, which means that 212 is divisible by 2. Divisibility by 3: The sum of the digits in the number 212 is 5. Since 5 is not divisible by 3, 212 is also not divisible by 3. Divisibility by 5: The unit’s place digit is 2. Therefore, 212 is not divisible by 5. Divisibility by 7: The last digit in 212 is 2. To check divisibility by 7, double the last digit (2 × 2 = 4). Then, subtract it from the rest of the number (21 - 4 = 17). Since 17 is not divisible by 7, 212 is also not divisible by 7. Divisibility by 11: In 212, the sum of the digits in odd positions is 3, and the sum of the digits in even positions is 1. This would mean that 212 is not divisible by 11. Since 212 is divisible only by 2 and 4, 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 1 to 100 in 10 rows and 10 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 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 from 1 to 100. Since 212 is greater than 100 and is not present in a basic list of prime numbers extended beyond 100, 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 212 as 2 × 106. Step 2: In 2 × 106, 106 is a composite number. Further, break the 106 into 2 × 53. Step 3: Now we get the product consisting of only prime numbers. Hence, the prime factorization of 212 is 2 × 2 × 53.

Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12. Prime numbers: Natural numbers greater than 1 that are divisible by only 2 numbers, 1 and itself, are called prime numbers. For example, 7 is a prime number because it is divisible by 1 and 7. Divisibility rules: Guidelines that help determine whether one number is divisible by another without performing division repeatedly. For example, a number is divisible by 2 if its last digit is even. Prime factorization: Breaking down a composite number into a product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3. Co-prime numbers: Two numbers having only 1 as a common factor are referred to as co-prime. For instance, 8 and 15 are co-prime numbers.