Is 998 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 998 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 998 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 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 998 is prime or composite.

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

Step 2: Divide 998 by 2. It is divisible by 2, so 2 is a factor of 998.

Step 3: Divide 998 by 3. It is not divisible by 3, so 3 is not a factor of 998.

Step 4: You can simplify checking divisors up to the square root of 998, which is approximately 31.6. We then need to only check divisors up to this value.

Step 5: When we divide 998 by numbers like 2, 499, and others up to 31.6, we find that it has factors in addition to 1 and itself. Since 998 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 is 8, an even number, which means that 998 is divisible by 2.

Divisibility by 3: The sum of the digits in the number 998 is 26. Since 26 is not divisible by 3, 998 is also not divisible by 3.

Divisibility by 5: The unit’s place digit is 8. Therefore, 998 is not divisible by 5.

Divisibility by 7: The number 998 is not divisible by 7 as it doesn't meet the divisibility rule for 7.

Divisibility by 11: In 998, the difference between the sum of the digits in odd positions and even positions is 8. This means that 998 is not divisible by 11. Since 998 is divisible by 2 and other numbers, 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 up to a certain limit in rows and columns.

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 multiples of 2.

Step 4: Mark 3 because it is a prime number and cross out all multiples of 3.

Step 5: Repeat this process with the next unmarked number until you have marked or crossed all numbers up to your limit. Through this process, we will have a list of prime numbers. 998 is not present in the list of prime numbers, so it is a composite number.

Prime factorization is the process of breaking down a number into its prime factors. Then multiply those factors to obtain the original number.

Step 1: We can write 998 as 2 × 499.

Step 2: Both 2 and 499 are prime numbers.

Step 3: Since the factorization includes more than one number, 998 is a composite number.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than 2 numbers are called composite numbers. For example, 998 is a composite number because it is divisible by 1, 2, 499, and 998.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves. For example, 3 is a prime number.

• Divisibility rules: A set of guidelines that help determine if a number is divisible by another number without performing the actual division.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 998 is 2 × 499.

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