Factors of 1001
2026-02-28 14:02 Diff
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Last updated on December 12, 2025

Factors are the ‘building blocks’ of a number. They are the numbers that can be multiplied together to reach the number you started with. 1001 is an interesting number. It is large enough to make you think, but simple enough to learn if you know a few tricks. Let’s dive into it!

What are the factors of 1001?

Factors are whole numbers that, when multiplied, the product is equal to 1001. 


1001 is not a prime number, its factors are 1,7,11,13,77,91,143,1001. For every factor, there is a corresponding negative factor, for 1001, the negative factors -1,-7,-11,-13,-77,-91,-143 and -1001.
 

How to find the factors of 1001?

There are various methods we apply to find the factors of any number. Few of them are listed here;  multiplication method, division method, prime factors and prime factorization and factor tree method. These are explained in detail below, let’s learn !

Finding Factors Using Multiplication

Step 1: Find all pairs of numbers whose product is 1001. 


Step 2: All the pairs found represent the factors of 1001. 


1001 is not a prime number. The pair of numbers whose product is 1001 is;


1×1001=1001 


7×143 = 1001


11×91=1001


13×77=1001


The factors of 1001 are 1,7,11,13,77,91,143,1001.
 

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Finding Factors by Division Method

Step 1: Start by dividing 1001 with the smallest number, and check the remainders. 


Step 2: 1001 is not prime, therefore the divisors it has are 1,7,11,13,77,91,143,1001. Any number that is further checked for divisibility leaves behind a remainder.


The factors of 1001 are 1,7,23 and 1001.
 

Prime factors and prime factorization

— 1001 is not a prime number.


— The prime factorization of 1001 is 7×11×13 = 1001


— Factors of 1001 are 1,7,11,13,77,91,143,1001.
 

Factor tree

— In this method, we make branches that extend from the number to express a number as the product of its factors. 


— In the case of 1001, only one branch will be extended as the number is prime factorized as 7×143 and factored further as 11×13 = 143. 11 and 13 are prime numbers and cannot be factored further. 
 

Common mistakes and how to avoid them in factors of 1001

We all make mistakes when it comes to finding factors, especially when it comes to numbers like 1001. Don’t worry, it is a part of learning. Here are a few common slip-ups we may make, along with tips to avoid them. 
 

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Problem 1

Find the prime factors of 1001.

Okay, lets begin

Start by dividing 1001 by the smallest prime number that divides it evenly.


1001÷7=143, so 7 is a factor.


Now, factorize 143.


143÷11=13, so 11 and 13 are also factors.


The prime factorization of 1001 is therefore: 7×11×13.
 

Explanation

Prime factorization means breaking down a number into its prime factors. We start with the smallest prime numbers and continue dividing until all remaining factors are prime. Here, 1001’s factors—7, 11, and 13—are all primes.
 

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Problem 2

What is the sum of all factors of 1001?

Okay, lets begin

List the factors of 1001, which are: 1, 7, 11, 13, 77, 91, 143, and 1001.


Add these factors: 1+7+11+13+77+91+143+1001=1344


The sum of all factors of 1001 is 1344.
 

Explanation

 Adding all factors of a number gives us their sum. We simply find each factor and add them up.
 

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Problem 3

Is 21 a factor of 1001?

Okay, lets begin

Divide 1001 by 21 to check if it results in a whole number. 1001÷21=47.666…


Since the result is not a whole number, 21 is not a factor of 1001.
 

Explanation

To verify if a number is a factor, divide 1001 by that number. If it divides evenly, it is a factor; if not, it isn’t. Here, 21 doesn’t divide evenly, so it isn’t a factor.
 

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FAQs on Factors of 1001

1.What is the prime factorization of 1001 and 385?

Prime factorization is breaking numbers down into their prime factors.
1001 = 7×11 ×13
385 = 5×7×11
 

2.What are the factors of 1001 and 910?

Factors of 1001: 1, 7, 11,13, 77, 91, 143 and 1001. 
Factors of 910: 1, 2, 5, 7, 10, 13, 14, 26, 35, 65, 70, 91, 130, 182, 455, 910.
The product of combinations of the above numbers give us the product of 1001 and 910 respectively. 
 

3.Is the cube root of 1001 rational?

The cube root of 1001 is 10.0033322228.
We cannot write 10.0033322228 in the form of p/q where q is not equal to zero, which is the condition for a number to be a rational number. 
 

4. What is the triple root of 1000?

A triple root is any number that is multiplied thrice to get the original number. In case of 1000 we can write the triple root as 10 10 10, 103 is 1000. 

5.What is the LCM of 1001 and 1008?

144144 is the smallest number that appears commonly on the lists of the numbers 1001 and 1008. 
LCM (1001,1008) = 144144
 

Important Glossaries for Factors of 1001

  • Factors: numbers that divide the given number without leaving a remainder. 
  • Prime factorization: breaking numbers down into their prime factors.
  • Prime factors: Prime numbers that multiply together to form a given number.
  • Composite number: Number that has at least more than one divisor other than 1 and the number itself.

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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.