Is 550 a Prime Number?

There are two types of numbers, mostly

• Prime numbers
   
• 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 550 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 550 has more than two factors, it is not a prime number. Few methods are used 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 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 550 is prime or composite.

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

Step 2: Divide 550 by 2. It is divisible by 2, so 2 is a factor of 550.

Step 3: Divide 550 by 3. It is not divisible by 3, so 3 is not a factor of 550.

Step 4: You can simplify checking divisors up to 550 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 550 by 2, 5, and 11, it is divisible by 2, 5, and 11. Since 550 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 value is 0. Zero is an even number, which means that 550 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 550 is 10. Since 10 is not divisible by 3, 550 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 0. Therefore, 550 is divisible by 5.

Divisibility by 7: The last digit in 550 is 0. To check divisibility by 7, double the last digit (0 × 2 = 0). Then, subtract it from the rest of the number (55 - 0 = 55). Since 55 is not divisible by 7, 550 is also not divisible by 7.

Divisibility by 11: In 550, the sum of the digits in odd positions is 5, and the sum of the digits in even positions is 5. Since the difference is 0, which is divisible by 11, 550 is divisible by 11.

Since 550 is divisible by 2, 5, and 11, 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.

The list is 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.

550 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 550 as 2 × 275.

Step 2: In 2 × 275, 275 is a composite number. Further, break 275 into 5 × 55.

Step 3: Continue breaking down 55 into 5 × 11.

Step 4: Now, we get the product consisting of only prime numbers. Hence, the prime factorization of 550 is 2 × 5 × 5 × 11.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 550 is a composite number because it is divisible by 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, and 550.
   
• Prime numbers: A natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 7 is a prime number because it is divisible only by 1 and 7.
   
• Divisibility rules: A shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division. For instance, a number is divisible by 5 if its last digit is 0 or 5.
   
• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 550 is 2 × 5 × 5 × 11.
   
• Factors: Numbers that divide another number exactly without leaving a remainder are called factors. For example, 1, 2, 5, 10, 11, 22, 25, 50, 55, 110, 275, and 550 are factors of 550.