Is 9997 a prime number?

The number 9997 has a set of factors, and these factors are capable of dividing the number completely without leaving any remainder. Thus, we need to check whether 9997 is divisible by any numbers other than 1 and 9997 itself to determine if it is a prime or non-prime number.

A number to be a prime number should follow the criteria that it should not have factors other than 1 and the number itself. If 9997 has any divisors other than 1 and itself, it is a composite number. Below are the methods we can use to check if 9997 is a prime or composite number.

The different methods we can use to check if a number is a prime number are explained below:

1. Counting Divisors Method
2. Divisibility Test
3. Prime Number Chart
4. Prime Factorization
    

For the counting divisors method, we need to check whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 9997 would simply be: Divisors of 9997 = 1, 9997 Number of divisors = 2

Since 9997 only has two divisors, it is considered a prime number.
 

 In the division method, we try to divide the number by any of the prime numbers. If we cannot find a divisor, then it is considered a prime number. The divisors of 9997 are only 1 and 9997, making it a prime number.
 

The prime number chart is the list of prime numbers starting from 2 to infinity.

The list of prime numbers under 100 are: 2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Since 9997 is not present in the list and doesn’t have any divisors other than 1 and itself, it is a prime number.

• Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 9997 is a prime number because it can only be divided by 1 and 9997.

• Divisors: The numbers that can divide another number exactly without leaving a remainder. The divisors of a prime number are always 1 and the number itself.

• Composite Number: A positive integer greater than 1 that has more than two divisors. Unlike prime numbers, composite numbers can be divided by numbers other than 1 and itself.

• Divisibility Test: A method used to determine if a number can be divided by another number without a remainder. This test helps determine whether a number is prime or composite.

• Prime Factorization: Breaking down a number into its prime factors. For a prime number like 9997, its prime factorization is the number itself because it has no other divisors.