Is 547 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, which is 1.

Since 547 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 547 has exactly two factors, it is 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 547 is prime or composite.

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

Step 2: Check divisibility by prime numbers up to the square root of 547 (approximately 23.4).

Step 3: 547 is not divisible by any prime numbers like 2, 3, 5, 7, 11, 13, 17, 19, or 23. Since 547 has only two divisors, it is a prime 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: 547 is odd, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in the number 547 is 16. Since 16 is not divisible by 3, 547 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 7, so 547 is not divisible by 5.

Divisibility by 7: For 547, (54 - 2×7 = 40), which is not divisible by 7.

Divisibility by 11: The alternating sum of the digits is (5 - 4 + 7 = 8), which is not divisible by 11. Since 547 is not divisible by any of these, it is a prime 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 in a grid format.

Step 2: Leave 1 without marking, 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 for subsequent prime numbers. Through this process, we have a list of prime numbers, and 547 is found to be a prime 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: Attempt to divide 547 by the smallest prime 2, but it is not divisible.

Step 2: Attempt to divide 547 by subsequent primes like 3, 5, 7, etc., and find no divisors.

Step 3: Since no prime numbers divide 547, it has no factors other than 1 and itself, confirming it is a prime number.

• Prime numbers: Natural numbers greater than 1 that have no divisors other than 1 and themselves.
   
• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers.
   
• Divisibility rules: Guidelines that help determine if one number is divisible by another without performing full division.
   
• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.
   
• Co-prime numbers: Two numbers that have no common factors other than 1.