Is 534 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 534 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 534 has more than two factors, it is not a prime number.

Several methods are used to distinguish between prime and composite numbers.

Some 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 534 is prime or composite.

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

Step 2: Divide 534 by 2. It is divisible by 2, so 2 is a factor of 534.

Step 3: Divide 534 by 3. It is divisible by 3, so 3 is a factor of 534.

Step 4: You can simplify checking divisors up to 534 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 534 by 2, 3, and other numbers, it is divisible by 2 and 3.

Since 534 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, which is even, so 534 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 534 is 12. Since 12 is divisible by 3, 534 is also divisible by 3.

Divisibility by 5: The unit’s place digit is 4. Therefore, 534 is not divisible by 5.

Divisibility by 7: Using the divisibility rule for 7, 534 is not divisible by 7.

Divisibility by 11: In 534, the sum of the digits in odd positions is 8, and the sum of the digits in even positions is 3. The difference is 5, which is not divisible by 11. Since 534 is divisible by 2 and 3, 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 grid format.

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 a table consisting of marked and crossed boxes, except 1. Through this process, we will have a list of prime numbers.

Since 534 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 534 as 2 × 267.

Step 2: In 2 × 267, 267 is a composite number. Further, break 267 into 3 × 89.

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

Hence, the prime factorization of 534 is 2 × 3 × 89.

• 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 numbers: Natural numbers greater than 1 that have only two factors, 1 and themselves. For example, 7 is a prime number.

• Divisibility: The ability of one number to be divided by another without leaving a remainder.

• Factors: Numbers that divide another number exactly without leaving a remainder. For example, the factors of 4 are 1, 2, and 4.

• Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 18 is 2 × 3 × 3.