214 LearnersLast updated on May 26th, 2025
Factors of 1001
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.
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.
Mistake 1
Excluding negative factors
Every positive factor has a corresponding negative factor. Often times, the negative factors are not included.
Factors of 1001 Examples
Problem 1
Find the prime factors of 1001.
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.
Problem 2
What is the sum of all factors of 1001?
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.
Problem 3
Is 21 a factor of 1001?
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.
FAQs on Factors of 1001
1.What is the prime factorization of 1001 and 385?
2.What are the factors of 1001 and 910?
3.Is the cube root of 1001 rational?
4. What is the triple root of 1000?
5.What is the LCM of 1001 and 1008?
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.
