Is 272 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, 5 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, 8 is divisible by 1, 2, 4, and 8, 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 272 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 272 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 would be prime.
   
• If the count is more than 2, then the number is composite.

Let’s check whether 272 is prime or composite.

Step 1: All numbers are divisible by 1 and itself. 

Step 2: Divide 272 by 2. It is divisible by 2, so 2 is a factor of 272. 

Step 3: Continue checking divisibility by successive integers.

Since 272 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 is 2, which is an even number, meaning that 272 is divisible by 2.

Divisibility by 3: The sum of the digits in 272 is 11. Since 11 is not divisible by 3, 272 is also not divisible by 3. 

Divisibility by 4: The last two digits of 272 are 72, which is divisible by 4. Therefore, 272 is divisible by 4.

Divisibility by 5: The unit’s place digit is 2. Therefore, 272 is not divisible by 5.

Since 272 is divisible by more than two numbers, 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 sequentially. 

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 the next uncrossed number (3) and cross out all its multiples.

Step 5: Repeat this process until the desired range is covered. Through this process, we will have a list of prime numbers.

Since 272 is not present in this list, 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 272 as 2 × 136.

Step 2: In 2 × 136, 136 is a composite number. Further, break 136 into 2 × 68.

Step 3: Continue factorization: 68 = 2 × 34, and 34 = 2 × 17.

Step 4: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 272 is 2 × 2 × 2 × 2 × 17.

• 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 it is divisible by 1, 2, 3, 4, 6, and 12.
   
• Prime Numbers: Natural numbers greater than 1 with only two factors, 1 and the number itself. For example, 11 is a prime number.
   
• Divisibility: The ability of one number to be divided by another without a remainder. For example, 15 is divisible by 5.
   
• Prime factorization: Expressing a number as a product of prime numbers. For example, the prime factorization of 30 is 2 × 3 × 5. 
   
• Sieve of Eratosthenes: A method to find all prime numbers up to a certain limit by progressively marking the multiples of each prime number starting from 2.