Factors of 1003
2026-02-28 08:06 Diff
https://brightchamps.com/en-us/math/numbers/factors-of-1003

252 Learners

Last updated on December 12, 2025

Factors are the numbers that divide any given number evenly without 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 1003, how they are used in real life, and tips to learn them quickly.

What are the Factors of 1003?

The numbers that divide 1003 evenly are known as factors of 1003.

A factor of 1003 is a number that divides the number without a remainder.

The factors of 1003 are 1, 17, 59, and 1003.

Negative factors of 1003: -1, -17, -59, and -1003.

Prime factors of 1003: 17 and 59.

Prime factorization of 1003: 17 × 59.

The sum of factors of 1003: 1 + 17 + 59 + 1003 = 1080

How to Find Factors of 1003?

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

  • Finding factors using multiplication
     
  • Finding factors using the division method
     
  • Prime factors and Prime factorization

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1003. Identifying the numbers which are multiplied to get the number 1003 is the multiplication method.

Step 1: Multiply 1003 by 1, 1003 × 1 = 1003.

Step 2: Check for other numbers that give 1003 after multiplying 17 × 59 = 1003

Therefore, the positive factor pairs of 1003 are: (1, 1003) and (17, 59).

All these factor pairs result in 1003.

For every positive factor, there is a negative factor.

Explore Our Programs

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 as whole numbers as factors. Factors can be calculated by following a simple division method:

Step 1: Divide 1003 by 1, 1003 ÷ 1 = 1003.

Step 2: Continue dividing 1003 by the numbers until the remainder becomes 0.

1003 ÷ 1 = 1003

1003 ÷ 17 = 59

1003 ÷ 59 = 17

Therefore, the factors of 1003 are: 1, 17, 59, 1003.

Prime Factors and Prime Factorization

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

Using Prime Factorization: In this process, prime factors of 1003 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

1003 ÷ 17 = 59

59 ÷ 59 = 1

The prime factors of 1003 are 17 and 59.

The prime factorization of 1003 is: 17 × 59.

Factor Tree

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

Step 1: Firstly, 1003 is divided by 17 to get 59.

Step 2: Now divide 59 by 59 to get 1. Here, 59 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 1003 is: 17 × 59.

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 1003: (1, 1003) and (17, 59).

Negative factor pairs of 1003: (-1, -1003) and (-17, -59).

Common Mistakes and How to Avoid Them in Factors of 1003

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

Download Worksheets

Problem 1

There are 17 people and 1003 candies. How will they divide it equally?

Okay, lets begin

They will get 59 candies each.

Explanation

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

1003/17 = 59

Well explained 👍

Problem 2

A rectangular painting has a length of 17 inches and a total area of 1003 square inches. Find the width.

Okay, lets begin

59 inches.

Explanation

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

Area = length × width

1003 = 17 × width

To find the value of width, we need to shift 17 to the left side.

1003/17 = width

Width = 59.

Well explained 👍

Problem 3

There are 59 boxes and 1003 apples. How many apples will be in each box?

Okay, lets begin

Each box will have 17 apples.

Explanation

To find the apples in each box, divide the total apples with the boxes.

1003/59 = 17

Well explained 👍

Problem 4

In a class, there are 1003 students, and 17 groups. How many students are there in each group?

Okay, lets begin

There are 59 students in each group.

Explanation

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

1003/17 = 59

Well explained 👍

Problem 5

1003 books need to be arranged in 59 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 17 books.

Explanation

Divide total books with shelves.

1003/59 = 17

Well explained 👍

FAQs on Factors of 1003

1.What are the factors of 1003?

1, 17, 59, 1003 are the factors of 1003.

2.Mention the prime factors of 1003.

The prime factors of 1003 are 17 × 59.

3.Is 1003 a multiple of 17?

4.Mention the factor pairs of 1003?

(1, 1003) and (17, 59) are the factor pairs of 1003.

5.What is the square of 1003?

The square of 1003 is 1,006,009.

Important Glossaries for Factors of 1003

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1003 are 1, 17, 59, and 1003.
     
  • Prime factors: The factors which are prime numbers. For example, 17 and 59 are prime factors of 1003.
     
  • 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 1003 are (1, 1003) and (17, 59).
     
  • Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 1003 is 17 × 59.
     
  • Negative factors: Factors that are negative counterparts of positive factors. For example, -1, -17, -59, and -1003 are negative factors of 1003.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.