Factors of 1009
2026-02-28 00:44 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-1009

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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. 1009 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 1009?

Factors are whole numbers that, when multiplied, the product is equal to 1009. 


1009 is a prime number, its only factors are 1 and 1009. For every factor, there is a corresponding negative factor, for 1009, the negative factors -1, -1009. 
 

How to find the factors of 1009?

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 1009. 


Step 2: All the pairs found represent the factors of 1009. 


1009 is a prime number. The only pair of numbers whose product is 1009 is 1×1009=1009. 
The factors of 1009 are 1 and 1009 only. 

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Finding Factors by Division Method

Step 1: Start by dividing 1009 with the smallest number, and check the remainders. 


Step 2: 1009 is prime, therefore the only divisors it has are 1 and 1009. Any number that is further checked for divisibility leaves behind a remainder.


The factors of 1009 are 1 and 1009 only. 
 

Prime factors and prime factorization

— 1009 is a prime number.


— The prime factorization of 1009 is 1009 times 1. 


— Factors of 1009 are 1,1009
 

Factor tree

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


— In case of 1009, only one branch will be extended as there are no other factors of the number.
 

Common mistakes and how to avoid them in the factors of 1009

We all make mistakes when it comes to finding factors, especially when it comes to numbers like 1009. 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

Is 7 a factor of 1009?

Okay, lets begin

To check if 7 is a factor, divide 1009 by 7.


1009÷7=144.14 (not a whole number).


Since the result isn’t a whole number, 7 is not a factor of 1009.
 

Explanation

 A factor of 1009 must divide evenly into 1009 without leaving any remainder. Since 7 doesn’t do that, it’s not a factor.

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Problem 2

Is 1009 a prime number?

Okay, lets begin

To determine if 1009 is prime, we need to see if any whole numbers other than 1 and 1009 itself divide evenly into it.


Checking divisibility by smaller primes up to √1009≈31.8:


2: 1009 is odd, so not divisible by 2.


3: Sum of digits 1+0+0+9=101 + 0 + 0 + 9 = 101+0+0+9=10 (not divisible by 3).


5: 1009 doesn’t end in 0 or 5, so it’s not divisible by 5.


Checking through other primes (7, 11, 13, 17, etc.) reveals that none divide evenly.


Since no divisors are found, 1009 is a prime number.
 

Explanation

 A prime number has no factors other than 1 and itself. Testing divisibility up to  √1009 is enough to confirm this, as factors repeat after the square root.
 

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Problem 3

Which of the following is a factor of 1009: 1, 10, 100, 1009?

Okay, lets begin

The factors of 1009 are 1 and 1009 since it’s a prime number.


Among the options, only 1 and 1009 are factors.
 

Explanation

 Multiples and factors are different. Factors divide into 1009 without a remainder. Here, only 1 and 1009 do that, making them the correct choices.
 

Well explained 👍

FAQs on Factors of 1009

1. Is 1009 a twin prime?

No. 1009 is not a twin prime. Twin primes are any two consecutive prime numbers whose difference is 2. For example, 101 and 103 satisfy this. 
 

2. What is a prime number that follows 1009?

The prime number that falls after 1009 is 1013. It has only two factors which are the number and 1 only. 
 

3.What are the prime factors of 99?

The prime factors of 99 are 3,3 and 11. The number 99 is the product of the mentioned numbers, all that cannot be factorized further. 
 

4.What is the cube of 1009 ?

The cube of a number is multiplied by itself thrice. The cube of 1009 (10093) is 1027243729.


To verify if it is correct, we just divide the obtained cube by 3. 1027243729/3 = 1009. 
 

5.Is the cube root of 1009 rational?

The cube root of 1009 is 10.0299104473.


We cannot write 10.0299104473 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. 

Important Glossaries for Factors of 1009

  • 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.