Is 504 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 504 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 504 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 numbers as 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 504 is prime or composite.

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

Step 2: Divide 504 by 2. It is divisible by 2, so 2 is a factor of 504.

Step 3: Divide 504 by 3. It is divisible by 3, so 3 is a factor of 504.

Step 4: Simplify by checking divisors up to the square root of 504.

Step 5: When we divide 504 by 2, 3, 4, 6, 7, 8, 9, and more, it is divisible by these numbers.

Since 504 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 4. Four is an even number, which means that 504 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 504 is 9 (5 + 0 + 4 = 9). Since 9 is divisible by 3, 504 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 504 is not divisible by 5.

Divisibility by 7: Using the rule, the number 504 is divisible by 7.

Divisibility by 11: Check the alternating sum and difference of the digits. In 504, the alternating sum is 1 (5 - 0 + 4 = 9). Since 9 is not divisible by 11, 504 is not divisible by 11. Since 504 is divisible by multiple numbers other than 1 and itself, 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 numbers from 1 to 100 in 10 rows and 10 columns.

Step 2: Leave 1 unmarked, 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 end of the list. Through this process, we will have a list of prime numbers from 1 to 100.

504 is not present in the list of prime numbers up to 100, so it is a composite number.

Prime factorization is a process of breaking down a number into prime factors, then multiplying those factors to obtain the original number.

Step 1: We can write 504 as 2 × 252.

Step 2: In 2 × 252, 252 is a composite number. Further, break 252 into 2 × 126.

Step 3: Continue breaking down until only prime numbers are left.

The prime factorization of 504 is 2 × 2 × 2 × 3 × 3 × 7.

• 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 factorization: The process of breaking down a composite number into a product of its prime factors.

• Divisibility rules: Guidelines that help determine if one number is divisible by another.

• Sieve of Eratosthenes: An ancient algorithm used to find all prime numbers up to a specified integer.

• Co-prime numbers: Two numbers that have only 1 as their common factor.