Is 4001 a prime number?
2026-02-28 23:23 Diff
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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 4001 a prime number?

The number 4001 has got 9 factors, that are capable of dividing the number completely without leaving any remainder. Thus, the number 4001 is a non-prime number. The factors of 4001 include 1, 3, 7, 9, 27, 21, 133, 189, and 4001.


 

Why is 4001 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, 4001 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 4001 would simply be:


Divisors of 4001 = 1, 3, 7, 9, 27, 21, 133, 189, 4001
Number of divisors = 9


The number 4001 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, the prime number only has 2 divisors, which are 1 and itself.


The divisors of 4001 are 1, 3, 7, 9, 27, 21, 133, 189, and 4001.


Thus, 4001 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, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.


4001 is not present in the list, it is not a prime number.
 

Using the Prime Factorization Method

This method is only used for a non-prime number/composite number. Since 4001 is a composite number, the prime factorization for 4001 is:


Factors of 4001 = 3 × 7 × 19.
 

Common mistakes to avoid when determining if 4001 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 4001 a prime number":

1.What is the largest prime factor of 4001?

The largest prime factor of 4001 is 4001 itself, as it is a composite number.
 

2.What is the smallest prime factor of 4001?

The smallest prime factor of 4001 is 3.
 

3.Is 4001 a composite number?

Yes, 4001 is a composite number because it has divisors other than 1 and itself.
 

4.How to express 4001 as a product of prime factors?

4001 can be expressed as 3 × 1337.
 

5.Represent 4001 in the prime factor tree?

4001 → 3 × 1337 → 3 × 7 × 191.
 

6.Do any perfect squares exist in the prime factors of 4001?

7.Do any perfect cubes exist in the prime factors of 4001?

8.What can 4001 be divided by?

4001 can be divided by 1, 3, 7, 21, 191, 1337, and 4001.

Important Glossary for "Is 4001 a Prime Number?"

  • Prime Number: A number greater than 1 that has only two divisors: 1 and itself. For example, 2, 3, 5, and 7 are prime numbers. 4001 is not a prime number because it has more than two divisors.
  • Divisor: A number that divides another number exactly, leaving no remainder. For example, divisors of 4001 include 1, 3, 7, 9, 27, 21, 133, 189, and 4001.
  • Composite Number: A number that has more than two divisors. 4001 is a composite number because it has multiple divisors other than 1 and itself.
  • Prime Factorization: The process of expressing a number as a product of prime numbers. The prime factorization of 4001 is 3 × 7 × 19.
  • Divisibility Test: A method to check if a number can be divided by another number without leaving a remainder. For example, 4001 is divisible by 3, 7, and other numbers, which makes it a composite number.

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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.