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Last updated on May 26th, 2025

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Factors of 7000

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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 7000, how they are used in real life, and the tips to learn them quickly.

Factors of 7000 for Qatari Students
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What are the Factors of 7000?

The numbers that divide 7000 evenly are known as factors of 7000.

 

A factor of 7000 is a number that divides the number without remainder.

 

The factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, and 7000.

 

Negative factors of 7000: -1, -2, -4, -5, -7, -8, -10, -14, -20, -25, -28, -35, -40, -50, -56, -70, -100, -125, -140, -175, -200, -250, -280, -350, -500, -700, -875, -1000, -1400, -1750, -3500, and -7000.

 

Prime factors of 7000: 2, 5, and 7.

 

Prime factorization of 7000: 2³ × 5³ × 7.

 

The sum of factors of 7000: 1 + 2 + 4 + 5 + 7 + 8 + 10 + 14 + 20 + 25 + 28 + 35 + 40 + 50 + 56 + 70 + 100 + 125 + 140 + 175 + 200 + 250 + 280 + 350 + 500 + 700 + 875 + 1000 + 1400 + 1750 + 3500 + 7000 = 20176

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How to Find Factors of 7000?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 7000. Identifying the numbers which are multiplied to get the number 7000 is the multiplication method.

 

Step 1: Multiply 7000 by 1, 7000 × 1 = 7000.

 

Step 2: Check for other numbers that give 7000 after multiplying

 

2 × 3500 = 7000

4 × 1750 = 7000

5 × 1400 = 7000

7 × 1000 = 7000

8 × 875 = 7000

10 × 700 = 7000

14 × 500 = 7000

20 × 350 = 7000

25 × 280 = 7000

28 × 250 = 7000

35 × 200 = 7000

40 × 175 = 7000

50 × 140 = 7000

56 × 125 = 7000

70 × 100 = 7000

 

Therefore, the positive factor pairs of 7000 are: (1, 7000), (2, 3500), (4, 1750), (5, 1400), (7, 1000), (8, 875), (10, 700), (14, 500), (20, 350), (25, 280), (28, 250), (35, 200), (40, 175), (50, 140), (56, 125), (70, 100).

 

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

 

Step 1: Divide 7000 by 1, 7000 ÷ 1 = 7000.

 

Step 2: Continue dividing 7000 by the numbers until the remainder becomes 0.

 

7000 ÷ 1 = 7000

7000 ÷ 2 = 3500

7000 ÷ 4 = 1750

7000 ÷ 5 = 1400

7000 ÷ 7 = 1000

7000 ÷ 8 = 875

7000 ÷ 10 = 700

7000 ÷ 14 = 500

7000 ÷ 20 = 350

7000 ÷ 25 = 280

7000 ÷ 28 = 250

7000 ÷ 35 = 200

7000 ÷ 40 = 175

7000 ÷ 50 = 140

7000 ÷ 56 = 125

7000 ÷ 70 = 100

 

Therefore, the factors of 7000 are: 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, and 7000.

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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 7000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

7000 ÷ 2 = 3500

3500 ÷ 2 = 1750

1750 ÷ 2 = 875

875 ÷ 5 = 175

175 ÷ 5 = 35

35 ÷ 5 = 7

7 ÷ 7 = 1

 

The prime factors of 7000 are 2, 5, and 7.

 

The prime factorization of 7000 is: 2³ × 5³ × 7.

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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, 7000 is divided by 2 to get 3500.

 

Step 2: Now divide 3500 by 2 to get 1750.

 

Step 3: Then divide 1750 by 2 to get 875.

 

Step 4: Divide 875 by 5 to get 175.

 

Step 5: Divide 175 by 5 to get 35.

 

Step 6: Divide 35 by 5 to get 7. Here, 7 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 7000 is: 2³ × 5³ × 7.

 

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 7000: (1, 7000), (2, 3500), (4, 1750), (5, 1400), (7, 1000), (8, 875), (10, 700), (14, 500), (20, 350), (25, 280), (28, 250), (35, 200), (40, 175), (50, 140), (56, 125), (70, 100).

 

Negative factor pairs of 7000: (-1, -7000), (-2, -3500), (-4, -1750), (-5, -1400), (-7, -1000), (-8, -875), (-10, -700), (-14, -500), (-20, -350), (-25, -280), (-28, -250), (-35, -200), (-40, -175), (-50, -140), (-56, -125), (-70, -100).

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Common Mistakes and How to Avoid Them in Factors of 7000

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 the factors for every number. Always remember to include 1 and the number itself.

 

For example, in factors of 7000, 1 and 7000 are also factors.

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Factors of 7000 Examples

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Problem 1

A group of 14 people wants to buy 7000 candies for a festival. How many candies will each person get if they are divided equally?

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They will get 500 candies each.

Explanation

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

 

7000/14 = 500

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Problem 2

A rectangular garden has a length of 100 meters, and the total area is 7000 square meters. What is the width?

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70 meters.

Explanation

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

 

Area = length × width

 

7000 = 100 × width

 

To find the value of the width, we need to shift 100 to the left side.

 

7000/100 = width

 

Width = 70.

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Problem 3

There are 28 trucks and 7000 packages. How many packages will be in each truck?

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Each truck will have 250 packages.

Explanation

To find the packages in each truck, divide the total packages by the number of trucks.

 

7000/28 = 250

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Problem 4

A company has 7000 documents and 25 filing cabinets. How many documents can each cabinet hold?

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Each cabinet can hold 280 documents.

Explanation

Dividing the documents by the total cabinets, we will get the number of documents in each cabinet.

 

7000/25 = 280

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Problem 5

A library has 7000 books and 35 shelves. How many books will go on each shelf?

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Each of the shelves has 200 books.

Explanation

Divide total books by shelves.

 

7000/35 = 200

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FAQs on Factors of 7000

1.What are the factors of 7000?

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2.Mention the prime factors of 7000.

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3.Is 7000 a multiple of 5?

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4.Mention the factor pairs of 7000?

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5.What is the cube of 7000?

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6.How can children in Qatar use numbers in everyday life to understand Factors of 7000?

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7.What are some fun ways kids in Qatar can practice Factors of 7000 with numbers?

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8.What role do numbers and Factors of 7000 play in helping children in Qatar develop problem-solving skills?

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9.How can families in Qatar create number-rich environments to improve Factors of 7000 skills?

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Important Glossaries for Factors of 7000

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7000 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 125, 140, 175, 200, 250, 280, 350, 500, 700, 875, 1000, 1400, 1750, 3500, and 7000.
     
  • Prime factors: The factors which are prime numbers. For example, 2, 5, and 7 are prime factors of 7000.
     
  • 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 7000 are (1, 7000), (2, 3500), etc.
     
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 7000 is 2³ × 5³ × 7.
     
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find factor pairs of 7000 such as (10, 700).
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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 7000 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!
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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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