Is 1997 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 1997 has only two factors, it is a prime number.

The characteristic of a prime number is that it has only two divisors: 1 and itself. Since 1997 has only two factors, it is a prime number. A few 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 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 1997 is prime or composite.

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

Step 2: Check for divisors up to the square root of 1997, which is approximately 44.7. Since 1997 is not divisible by any number other than 1 and itself, it is a prime 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: 1997 is an odd number, so it is not divisible by 2.

Divisibility by 3: The sum of the digits in 1997 is 26. Since 26 is not divisible by 3, 1997 is not divisible by 3.

Divisibility by 5: The unit’s place digit is 7. Therefore, 1997 is not divisible by 5.

Divisibility by 7, 11, and other primes up to 44: None divide 1997 without a remainder. Since 1997 is not divisible by any of these, it is a prime 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 up to a certain range.

Step 2: Leave 1 without coloring or crossing, as it is neither prime nor composite.

Step 3: Mark the smallest number as prime and cross out all its multiples.

Step 4: Repeat until reaching the limit. Since 1997 is not crossed out and is itself part of the list of primes, it is a prime number.

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

Step 1: Start dividing 1997 by the smallest prime numbers.

Step 2: Continue until you find a prime factor. Since 1997 does not break down further into any prime factors, it confirms that 1997 is a prime number.

• Prime numbers: Natural numbers greater than 1 that are divisible only by 1 and themselves, like 2, 3, 5, 7, etc.

• Composite numbers: Natural numbers greater than 1 that are divisible by more than two numbers, like 4, 6, 9, etc.

• Divisibility rules: Set of rules to determine if one number is divisible by another without performing the actual division.

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

• Factors: Numbers that divide a given number exactly without leaving a remainder. For example, the factors of 6 are 1, 2, 3, and 6.