Is 9991 a prime number?

The number 9991 has more than 2 factors, which are capable of dividing the number completely without leaving any remainder. Thus, the number 9991 is a non-prime number. The factors of 9991 include 1, 13, 23, 47, 53, 91, 221, 1007, and 9991.

A number to be a prime number should follow the criteria that it should not have factors more than 2. Here, 9991 has more than 2 factors, hence making it a composite number.

Given below are a few ways that can be used to find prime or composite numbers.

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, it is to be checked whether the number is divisible by any numbers other than 1 and the number itself.

The counting divisors method for 9991 would simply be:

Divisors of 9991 = 1, 13, 23, 47, 53, 91, 221, 1007, 9991
Number of divisors = 9

The number 9991 can be considered composite.
 

In the division test, we try to divide the number by any of the prime numbers. If we cannot, then it is considered a prime number.

In the divisibility method, a prime number only has 2 divisors, which are 1 and itself.

The divisors of 9991 are 1, 13, 23, 47, 53, 91, 221, 1007, and 9991.

Thus, 9991 consists of 9 factors that divide it completely without any remainder.
 

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, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

9991 is not present in the list, so it is not a prime number.
 

This method is only used for a non-prime number/composite number. Since 9991 is a composite number, the prime factorization for 9991 is:

Factors of 9991 = 13 × 23 × 47
 

• Prime Number: A number greater than 1 that has no positive divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers.

• Composite Number: A number that has more than two divisors, meaning it can be divided by numbers other than 1 and itself. For example, 6 and 9991 are composite numbers.

• Divisibility Test: A method used to determine whether a number can be divided by another number without leaving a remainder. It helps in identifying factors of a number.

• Prime Factorization: The process of breaking down a composite number into its prime factors. For example, the prime factorization of 9991 is 13 × 23 × 47.

• Divisors: The numbers that divide a given number completely without leaving a remainder. For 9991, its divisors are 1, 13, 23, 47, 53, 91, 221, 1007, and 9991.