BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon100 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Factors of 3400

Professor Greenline Explaining Math Concepts

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 3400, how they are used in real life, and tips to learn them quickly.

Factors of 3400 for Qatari Students
Professor Greenline from BrightChamps

What are the Factors of 3400?

The numbers that divide 3400 evenly are known as factors of 3400.

 

A factor of 3400 is a number that divides the number without a remainder.

 

The factors of 3400 are 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, and 3400.

 

Negative factors of 3400: -1, -2, -4, -5, -10, -17, -20, -25, -34, -50, -68, -85, -100, -136, -170, -200, -340, -425, -680, -850, -1700, and -3400.

 

Prime factors of 3400: 2, 5, and 17.

 

Prime factorization of 3400: 22 × 52 × 17.

 

The sum of the factors of 3400: 1 + 2 + 4 + 5 + 10 + 17 + 20 + 25 + 34 + 50 + 68 + 85 + 100 + 136 + 170 + 200 + 340 + 425 + 680 + 850 + 1700 + 3400 = 8352

Professor Greenline from BrightChamps

How to Find Factors of 3400?

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

 

  • Finding factors using multiplication

     
  • Finding factors using division method

     
  • Prime factors and Prime factorization
Professor Greenline from BrightChamps

Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 3400. Identifying the numbers which are multiplied to get the number 3400 is the multiplication method.

 

Step 1: Multiply 3400 by 1, 3400 × 1 = 3400.

 

Step 2: Check for other numbers that give 3400 after multiplying

2 × 1700 = 3400

4 × 850 = 3400

5 × 680 = 3400

10 × 340 = 3400

20 × 170 = 3400

25 × 136 = 3400

34 × 100 = 3400

50 × 68 = 3400

 

Therefore, the positive factor pairs of 3400 are: (1, 3400), (2, 1700), (4, 850), (5, 680), (10, 340), (20, 170), (25, 136), (34, 100), (50, 68). For every positive factor, there is a negative factor.

Professor Greenline from BrightChamps

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 3400 by 1, 3400 ÷ 1 = 3400.

 

Step 2: Continue dividing 3400 by the numbers until the remainder becomes 0.

3400 ÷ 1 = 3400

3400 ÷ 2 = 1700

3400 ÷ 4 = 850

3400 ÷ 5 = 680

3400 ÷ 10 = 340

3400 ÷ 20 = 170

3400 ÷ 25 = 136

3400 ÷ 34 = 100

3400 ÷ 50 = 68

 

Therefore, the factors of 3400 are: 1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400.

Professor Greenline from BrightChamps

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:

 

  • Using prime factorization
  • Using factor tree

 

Using Prime Factorization: In this process, prime factors of 3400 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

3400 ÷ 2 = 1700

1700 ÷ 2 = 850

850 ÷ 2 = 425

425 ÷ 5 = 85

85 ÷ 5 = 17

17 ÷ 17 = 1

 

The prime factors of 3400 are 2, 5, and 17.

 

The prime factorization of 3400 is: 2^2 × 5^2 × 17.

Professor Greenline from BrightChamps

Factor Tree

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

 

Step 1: Firstly, 3400 is divided by 2 to get 1700.

 

Step 2: Now divide 1700 by 2 to get 850.

 

Step 3: Then divide 850 by 2 to get 425.

 

Step 4: Divide 425 by 5 to get 85.

 

Step 5: Divide 85 by 5 to get 17. Here, 17 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 3400 is: 2^2 × 5^2 × 17.

 

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 3400: (1, 3400), (2, 1700), (4, 850), (5, 680), (10, 340), (20, 170), (25, 136), (34, 100), and (50, 68).

 

Negative factor pairs of 3400: (-1, -3400), (-2, -1700), (-4, -850), (-5, -680), (-10, -340), (-20, -170), (-25, -136), (-34, -100), and (-50, -68).

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in Factors of 3400

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

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting the number itself and 1 is a factor

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 3400, 1 and 3400 are also factors.

Max from BrightChamps Saying "Hey"

Factors of 3400 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

A charity wants to distribute 3400 meals equally among 10 shelters. How many meals will each shelter receive?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Each shelter will receive 340 meals.

Explanation

To divide the meals equally, we need to divide the total meals by the number of shelters.

3400/10 = 340

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A rectangular park has a length of 50 meters and a total area of 3400 square meters. Find the width.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

68 meters.

Explanation

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

Area = length × width

3400 = 50 × width

To find the value of width, we need to shift 50 to the left side.

3400/50 = width

Width = 68.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

There are 3400 chairs, and they need to be arranged in 100 rows. How many chairs will be in each row?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Each row will have 34 chairs.

Explanation

To find the number of chairs in each row, divide the total chairs by the number of rows.

3400/100 = 34

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

In a company, there are 3400 employees and 50 departments. How many employees are there in each department?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

There are 68 employees in each department.

Explanation

Dividing the employees by the total departments, we will get the number of employees in each department.

3400/50 = 68

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

A library has 3400 books to be arranged on 200 shelves. How many books will go on each shelf?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Each of the shelves has 17 books.

Explanation

Divide total books by shelves.

3400/200 = 17

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Factors of 3400

1.What are the factors of 3400?

Math FAQ Answers Dropdown Arrow

2.Mention the prime factors of 3400.

Math FAQ Answers Dropdown Arrow

3.Is 3400 a multiple of 5?

Math FAQ Answers Dropdown Arrow

4.Mention the factor pairs of 3400?

Math FAQ Answers Dropdown Arrow

5.What is the square of 3400?

Math FAQ Answers Dropdown Arrow

6.How can children in Qatar use numbers in everyday life to understand Factors of 3400?

Math FAQ Answers Dropdown Arrow

7.What are some fun ways kids in Qatar can practice Factors of 3400 with numbers?

Math FAQ Answers Dropdown Arrow

8.What role do numbers and Factors of 3400 play in helping children in Qatar develop problem-solving skills?

Math FAQ Answers Dropdown Arrow

9.How can families in Qatar create number-rich environments to improve Factors of 3400 skills?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Factor of 3400

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 3400 are 1, 2, 4, 5, 10, 17, 20, etc.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 5, and 17 are prime factors of 3400.

 

  • Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 3400 is 22 × 52 × 17.

 

  • 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 3400 are (1, 3400), (2, 1700), etc.

 

  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give a particular product.
Professor Greenline from BrightChamps

About BrightChamps in Qatar

At BrightChamps, numbers are more than symbols—they open pathways to countless chances! Our mission is to help kids throughout Qatar master important math skills, focusing today on Factors of 3400 with special attention to factors—in an engaging, clear, and fun way. Whether your child is figuring out the speed of a ride at Angry Birds World, tracking local football scores, or managing their allowance for gadgets, strong number skills boost their confidence for daily tasks. Our interactive lessons make learning straightforward and enjoyable. Since kids in Qatar learn uniquely, we customize lessons to each child’s needs. From Doha’s modern cityscape to desert surroundings, BrightChamps brings math to life across Qatar. Let’s make factors an exciting part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: She loves to read number jokes and games.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom