Is 280 a Prime Number?

There are two types of numbers —

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 have a few properties such as:

• 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: 1.
  
   
• As 280 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 280 has more than two factors, it is not a prime number. There are several methods to distinguish between prime and composite numbers. A few methods are:

• 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 prime and composite numbers. 

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 280 is prime or composite.

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

Step 2: Divide 280 by 2. It is divisible by 2, so 2 is a factor of 280. -

Step 3: Divide 280 by 3. It is not divisible by 3, so 3 is not a factor of 280. 

Step 4: You can simplify checking divisors up to 280 by finding the square root value. We then need to check divisors only up to the root value. 

Step 5: When we divide 280 by 2, 4, 5, 7, 8, 10, and 14, it is divisible by these numbers.

Since 280 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 one's place value is 0. Zero is an even number, which means that 280 is divisible by 2. 

Divisibility by 3: The sum of the digits in the number 280 is 10. Since 10 is not divisible by 3, 280 is also not divisible by 3. 

Divisibility by 5: The unit’s place digit is 0. Therefore, 280 is divisible by 5. 

Divisibility by 7: To check divisibility by 7, double the last digit (0 × 2 = 0). Then, subtract it from the rest of the number (28 - 0 = 28). Since 28 is divisible by 7, 280 is also divisible by 7. 

Divisibility by 11: In 280, the sum of the digits in odd positions is 2, and the sum of the digits in even positions is 8. The difference is 6, which means 280 is not divisible by 11.

Since 280 is divisible by numbers other than 1 and itself, it has more than two factors, making it 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. The list includes 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

280 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 280 as 2 × 140. 

Step 2: In 2 × 140, 140 is a composite number. Further, break the 140 into 2 × 70.

Step 3: Break 70 into 2 × 35.

Step 4: Finally, break 35 into 5 × 7. Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 280 is 2 × 2 × 2 × 5 × 7.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 280 is a composite number because it is divisible by 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280. 
  
   
• Prime numbers: Natural numbers greater than 1 with no divisors other than 1 and themselves. For example, 7 is a prime number because it is only divisible by 1 and 7.
  
   
• Divisibility rules: Guidelines to determine if a number is divisible by another without performing division. For example, a number is divisible by 5 if its last digit is 0 or 5.
  
   
• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 10 are 1, 2, 5, and 10. 
  
   
• Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 28 is 2 × 2 × 7.