Is 1018 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 1018 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 1018 has more than two factors, it is not a prime number. A few methods are used to distinguish between prime and composite numbers:

• 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 1018 is prime or composite.

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

Step 2: Divide 1018 by 2. It is divisible by 2, so 2 is a factor of 1018.

Step 3: Divide 1018 by 3. It is not divisible by 3, so 3 is not a factor of 1018.

Step 4: You can simplify checking divisors up to 1018 by finding the root value. We then need to only check divisors up to the root value.

Step 5: When we divide 1018 by 2, it is divisible by 2.

Since 1018 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 8. Since 8 is an even number, 1018 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 1018 is 10. Since 10 is not divisible by 3, 1018 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 1018 is not divisible by 5.

Divisibility by 7: The last digit in 1018 is 8. To check divisibility by 7, double the last digit (8 × 2 = 16). Then subtract it from the rest of the number (101 - 16 = 85). Since 85 is not divisible by 7, 1018 is not divisible by 7.

Divisibility by 11: In 1018, the sum of the digits in odd positions is 9, and the sum of the digits in even positions is 1. This would mean that 1018 is not divisible by 11. Since 1018 is divisible by 2, 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 1000 in rows and columns as appropriate.

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 up to 1000.

1018 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 multiplying those factors to obtain the original number.

Step 1: We can write 1018 as 2 × 509.

Step 2: Check if 509 is a prime number. Since it is not divisible by any prime number up to its square root, 509 is a prime number.

Hence, the prime factorization of 1018 is 2 × 509.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 7 is a prime number.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers. For example, 12 is a composite number because 12 is divisible by 1, 2, 3, 4, 6, and 12.

• Divisibility rules: Rules that help determine if one number is divisible by another without performing division. For example, a number is divisible by 3 if the sum of its digits is divisible by 3.

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

• Co-prime numbers: Two numbers that have only 1 as a common factor. For example, 8 and 15 are co-prime numbers.