Factors of 3003
2026-02-28 13:07 Diff

234 Learners

Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without a remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 3003, how they are used in real life, and tips to learn them quickly.

What are the Factors of 3003?

The numbers that divide 3003 evenly are known as factors of 3003.

A factor of 3003 is a number that divides the number without a remainder.

The factors of 3003 are 1, 3, 7, 11, 21, 33, 77, 231, 273, 1001, and 3003.

Negative factors of 3003: -1, -3, -7, -11, -21, -33, -77, -231, -273, -1001, and -3003.

Prime factors of 3003: 3, 7, and 11.

Prime factorization of 3003: 3 × 7 × 11 × 13.

The sum of factors of 3003: 1 + 3 + 7 + 11 + 21 + 33 + 77 + 231 + 273 + 1001 + 3003 = 3661

How to Find Factors of 3003?

Factors can be found using different methods. Mentioned below are some commonly used methods:

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 3003. Identifying the numbers which are multiplied to get the number 3003 is the multiplication method.

Step 1: Multiply 3003 by 1, 3003 × 1 = 3003.

Step 2: Check for other numbers that give 3003 after multiplying

3 × 1001 = 3003

7 × 429 = 3003

11 × 273 = 3003

13 × 231 = 3003

21 × 143 = 3003

Therefore, the positive factor pairs of 3003 are: (1, 3003), (3, 1001), (7, 429), (11, 273), (13, 231), and (21, 143). For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method:

Step 1: Divide 3003 by 1, 3003 ÷ 1 = 3003.

Step 2: Continue dividing 3003 by the numbers until the remainder becomes 0.

3003 ÷ 1 = 3003

3003 ÷ 3 = 1001

3003 ÷ 7 = 429

3003 ÷ 11 = 273

3003 ÷ 13 = 231

Therefore, the factors of 3003 are: 1, 3, 7, 11, 13, 21, 33, 77, 231, 273, 1001, 3003.

Prime Factors and Prime Factorization

The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:

rime Factorization: In this process, prime factors of 3003 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

3003 ÷ 3 = 1001

1001 ÷ 7 = 143

143 ÷ 11 = 13

13 ÷ 13 = 1

The prime factors of 3003 are 3, 7, 11, and 13.

The prime factorization of 3003 is: 3 × 7 × 11 × 13.

Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -

Step 1: Firstly, 3003 is divided by 3 to get 1001.

Step 2: Now divide 1001 by 7 to get 143.

Step 3: Then divide 143 by 11 to get 13. Here, 13 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 3003 is: 3 × 7 × 11 × 13.

Factor Pairs: Two numbers that are multiplied to give a specific number are called factor pairs. Both positive and negative factors constitute factor pairs.

Positive factor pairs of 3003: (1, 3003), (3, 1001), (7, 429), (11, 273), (13, 231), and (21, 143).

Negative factor pairs of 3003: (-1, -3003), (-3, -1001), (-7, -429), (-11, -273), (-13, -231), and (-21, -143).

Common Mistakes and How to Avoid Them in Factors of 3003

Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.

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Problem 1

There are 3 friends and 3003 candies. How will they divide it equally?

Okay, lets begin

They will get 1001 candies each.

Explanation

To divide the candies equally, we need to divide the total candies with the number of friends.

3003/3 = 1001

Well explained 👍

Problem 2

A rectangular field has a length of 11 meters and a total area of 3003 square meters. Find the width?

Okay, lets begin

273 meters.

Explanation

To find the width of the field, we use the formula,

Area = length × width

3003 = 11 × width

To find the value of width, we need to shift 11 to the left side.

3003/11 = width

Width = 273.

Well explained 👍

Problem 3

There are 231 bags and 3003 candies. How many candies will be in each bag?

Okay, lets begin

Each bag will have 13 candies.

Explanation

To find the candies in each bag, divide the total candies with the bags.

3003/231 = 13

Well explained 👍

Problem 4

In a class, there are 3003 students, and 7 groups. How many students are there in each group?

Okay, lets begin

There are 429 students in each group.

Explanation

Dividing the students with the total groups, we will get the number of students in each group.

3003/7 = 429

Well explained 👍

Problem 5

There are 1001 books to be arranged in 3 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 333 books.

Explanation

Divide total books with shelves.

1001/3 = 333

Well explained 👍

FAQs on Factors of 3003

1.What are the factors of 3003?

1, 3, 7, 11, 13, 21, 33, 77, 231, 273, 1001, 3003 are the factors of 3003.

2.Mention the prime factors of 3003.

The prime factors of 3003 are 3 × 7 × 11 × 13.

3.Is 3003 a multiple of 7?

4.Mention the factor pairs of 3003?

(1, 3003), (3, 1001), (7, 429), (11, 273), (13, 231), and (21, 143) are the factor pairs of 3003.

5.What is the square of 3003?

The square of 3003 is 9024009.

Important Glossaries for Factor of 3003

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3003 are 1, 3, 7, 11, 13, 21, 33, 77, 231, 273, 1001, and 3003.
  • Prime factors: The factors which are prime numbers. For example, 3, 7, 11, and 13 are prime factors of 3003.
  • Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 3003 are (1, 3003), (3, 1001), etc.
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 3003 is 3 × 7 × 11 × 13.
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to form the original number. For example, using multiplication, (3, 1001) is a factor pair of 3003.

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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.