Is 524 a Prime Number?

There are two main 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 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 524 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 524 has more than two factors, it is not a prime number.

Several methods can be 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 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 524 is prime or composite.

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

Step 2: Divide 524 by 2. It is divisible by 2, so 2 is a factor of 524.

Step 3: Checking further, 524 is also divisible by numbers like 4, 131, and 262.

Since 524 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 4. Four is an even number, which means that 524 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 524 is 11. Since 11 is not divisible by 3, 524 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 524 is not divisible by 5.

Divisibility by 7: Using the rule for 7, 524 is not divisible by 7.

Divisibility by 11: In 524, the alternating sum of the digits is 7. This means that 524 is not divisible by 11. Since 524 is divisible by numbers like 2 and others, 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 these steps:

Step 1: Write numbers in a range, for example, 1 to 1000.

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 have marked and crossed out all numbers except primes. Through this process, we have a list of prime numbers. As 524 is not present in the list of prime numbers, 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 524 as 2 × 262.

Step 2: In 2 × 262, 262 is a composite number. Further, break the 262 into 2 × 131.

Step 3: Now we get the product consisting of only prime numbers.

Hence, the prime factorization of 524 is 2 × 2 × 131.

• 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 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.

• Divisibility rules: Guidelines used to determine if a number is divisible by another number without performing division.

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

• Sieve of Eratosthenes: A method for finding all prime numbers up to a specified integer.