Is 9991 a prime number?
2026-02-28 01:04 Diff
https://brightchamps.com/en-us/math/numbers/is-9991-a-prime-number

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Last updated on August 5, 2025

Prime numbers have only 1 and the number itself as factors. They are used in digital security and in securing digital payments. The topics below will help you gain more knowledge on prime numbers and how they are categorized.

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.


 

Why is 9991 not a prime number?

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
     

Using the Counting Divisors Method

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.
 

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Using the Divisibility test Method

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.
 

Using the Prime Number Chart

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.
 

Using the Prime Factorization Method

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
 

Common mistakes to avoid when determining if 9991 is a prime number

It is highly likely we commit some mistakes due to confusion or unclear understanding. Let us look at possible mistakes we may make and try to avoid them.
 

FAQs for "Is 9991 a prime number"

1.Is 9991 a prime number?

No, 9991 is not a prime number

2.What are the factors of 9991?

9991 has factors: 1, 53, 187, 9991.
 

3.Is 9991 a composite number?

Yes, 9991 is a composite number because it has divisors other than 1 and itself.
 

4.How to express 9991 as a product of prime factors?

5.What is the largest prime factor of 9991?

The largest prime factor of 9991 is 53.
 

6.What is the smallest prime factor of 9991?

The smallest prime factor of 9991 is 53.
 

7.Do any perfect squares exist in the prime factors of 9991?

8.Do any perfect cubes exist in the prime factors of 9991?

9.What can 9991 be divided by?

9991 can be divided by 1, 53, 187, and 9991.
 

Important Glossary for "Is 9991 a Prime Number?"

  • 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.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.