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Last updated on May 26th, 2025

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Factors of 6000

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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 6000, how they are used in real life, and tips to learn them quickly.

Factors of 6000 for Indian Students
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What are the Factors of 6000?

The numbers that divide 6000 evenly are known as factors of 6000.

 

A factor of 6000 is a number that divides the number without remainder.

 

The factors of 6000 include 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, and 6000.

 

Negative factors of 6000: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -125, -150, -200, -240, -250, -300, -375, -400, -500, -600, -750, -1000, -1200, -1500, -2000, -3000, and -6000.

 

Prime factors of 6000: 2, 3, and 5.

 

Prime factorization of 6000: 24 × 3 × 53.

 

The sum of factors of 6000: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 30 + 40 + 48 + 50 + 60 + 75 + 80 + 100 + 120 + 125 + 150 + 200 + 240 + 250 + 300 + 375 + 400 + 500 + 600 + 750 + 1000 + 1200 + 1500 + 2000 + 3000 + 6000 = 22176

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How to Find Factors of 6000?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that multiply to give 6000. Identifying the numbers that are multiplied to get the number 6000 is the multiplication method.

 

Step 1: Multiply 6000 by 1, 6000 × 1 = 6000.

 

Step 2: Check for other numbers that give 6000 after multiplying:

 

2 × 3000 = 6000

3 × 2000 = 6000

4 × 1500 = 6000

5 × 1200 = 6000

6 × 1000 = 6000

8 × 750 = 6000

10 × 600 = 6000

12 × 500 = 6000

15 × 400 = 6000

16 × 375 = 6000

20 × 300 = 6000

24 × 250 = 6000

25 × 240 = 6000

30 × 200 = 6000

40 × 150 = 6000

48 × 125 = 6000

50 × 120 = 6000

60 × 100 = 6000

75 × 80 = 6000

 

Therefore, the positive factor pairs of 6000 are: (1, 6000), (2, 3000), (3, 2000), (4, 1500), (5, 1200), (6, 1000), (8, 750), (10, 600), (12, 500), (15, 400), (16, 375), (20, 300), (24, 250), (25, 240), (30, 200), (40, 150), (48, 125), (50, 120), (60, 100), (75, 80).

 

For every positive factor, there is a negative factor.

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Finding Factors Using Division Method

Dividing the given numbers with 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 6000 by 1, 6000 ÷ 1 = 6000.

 

Step 2: Continue dividing 6000 by the numbers until the remainder becomes 0.

 

6000 ÷ 1 = 6000

6000 ÷ 2 = 3000

6000 ÷ 3 = 2000

6000 ÷ 4 = 1500

6000 ÷ 5 = 1200

6000 ÷ 6 = 1000

6000 ÷ 8 = 750

6000 ÷ 10 = 600

6000 ÷ 12 = 500

6000 ÷ 15 = 400

6000 ÷ 16 = 375

6000 ÷ 20 = 300

6000 ÷ 24 = 250

6000 ÷ 25 = 240

6000 ÷ 30 = 200

6000 ÷ 40 = 150

6000 ÷ 48 = 125

6000 ÷ 50 = 120

6000 ÷ 60 = 100

6000 ÷ 75 = 80

 

Therefore, the factors of 6000 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 125, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 2000, 3000, 6000.

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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 6000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

6000 ÷ 2 = 3000

3000 ÷ 2 = 1500

1500 ÷ 2 = 750

750 ÷ 2 = 375

375 ÷ 3 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

 

The prime factors of 6000 are 2, 3, and 5.

 

The prime factorization of 6000 is: 24 × 3 × 53.

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Factor Tree

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

 

Step 1: Firstly, 6000 is divided by 2 to get 3000.

 

Step 2: Now divide 3000 by 2 to get 1500.

 

Step 3: Then divide 1500 by 2 to get 750.

 

Step 4: Divide 750 by 2 to get 375.

 

Step 5: Divide 375 by 3 to get 125.

 

Step 6: Divide 125 by 5 to get 25.

 

Step 7: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 6000 is: 24 × 3 × 53.

 

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 6000: (1, 6000), (2, 3000), (3, 2000), (4, 1500), (5, 1200), (6, 1000), (8, 750), (10, 600), (12, 500), (15, 400), (16, 375), (20, 300), (24, 250), (25, 240), (30, 200), (40, 150), (48, 125), (50, 120), (60, 100), (75, 80).

 

Negative factor pairs of 6000: (-1, -6000), (-2, -3000), (-3, -2000), (-4, -1500), (-5, -1200), (-6, -1000), (-8, -750), (-10, -600), (-12, -500), (-15, -400), (-16, -375), (-20, -300), (-24, -250), (-25, -240), (-30, -200), (-40, -150), (-48, -125), (-50, -120), (-60, -100), (-75, -80).

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Common Mistakes and How to Avoid Them in Factors of 6000

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

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Forgetting the number itself and 1 is a factor

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

 

For example, in factors of 6000, 1 and 6000 are also factors.

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Factors of 6000 Examples

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Problem 1

There are 6 employees in a company and 6000 files. How will they distribute the files equally?

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They will get 1000 files each.

Explanation

To distribute the files equally, we need to divide the total files by the number of employees.

 

6000/6 = 1000

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Problem 2

A garden has a rectangular area, the length of the garden is 150 meters, and the total area is 6000 square meters. Find the width?

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40 meters.

Explanation

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

 

Area = length × width

 

6000 = 150 × width

 

To find the value of width, we need to shift 150 to the left side.

 

6000/150 = width

 

Width = 40.

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Problem 3

There are 12 boxes and 6000 marbles. How many marbles will be in each box?

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Each box will have 500 marbles.

Explanation

To find the marbles in each box, divide the total marbles by the boxes.

 

6000/12 = 500

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Problem 4

In a concert, there are 6000 attendees, and they are divided into 60 sections. How many attendees are there in each section?

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There are 100 attendees in each section.

Explanation

Dividing the attendees by the total sections, we will get the number of attendees in each section.

 

6000/60 = 100

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Problem 5

6000 chairs need to be arranged in 150 rows. How many chairs will go in each row?

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Each row will have 40 chairs.

Explanation

Divide the total chairs by the number of rows.

 

6000/150 = 40

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FAQs on Factors of 6000

1.What are the factors of 6000?

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2.Mention the prime factors of 6000.

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3.Is 6000 a multiple of 4?

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4.Mention the factor pairs of 6000?

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5.What is the square of 6000?

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6.How can children in India use numbers in everyday life to understand Factors of 6000?

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7.What are some fun ways kids in India can practice Factors of 6000 with numbers?

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8.What role do numbers and Factors of 6000 play in helping children in India develop problem-solving skills?

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9.How can families in India create number-rich environments to improve Factors of 6000 skills?

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Important Glossaries for Factors of 6000

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 6000 are 1, 2, 3, 4, 5, 6, etc.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 6000.
     
  • 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 6000 are (1, 6000), (2, 3000), etc.
     
  • Prime factorization: A method of expressing a number as the product of its prime factors. For example, the prime factorization of 6000 is 24 × 3 × 53.
     
  • Multiples: Numbers that can be divided by a given number without leaving a remainder. For example, 6000 is a multiple of 2, 3, and 5.
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About BrightChamps in India

At BrightChamps, numbers mean more than just digits—they open pathways to endless opportunities! We’re here to help children all over India grasp crucial math skills, focusing on today’s Factors of 6000 with a special look at factors—in a way that’s enjoyable, simple, and interactive. Whether your child is calculating the speed of a train passing by, following scores in a cricket match, or managing their pocket money for new gadgets, knowing numbers helps build their confidence in daily life. Our hands-on lessons keep learning fun and easy. Since kids in India learn in many ways, we customize lessons to fit each learner. From Mumbai’s lively markets to Delhi’s vibrant streets, BrightChamps makes math meaningful and exciting all across India. Let’s turn factors into a fun part of every child’s math story!
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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.

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Fun Fact

: She loves to read number jokes and games.

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