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Last updated on May 26th, 2025

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Factors of 7500

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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 the items equally, arranging things, etc. In this topic, we will learn about the factors of 7500, how they are used in real life, and the tips to learn them quickly.

Factors of 7500 for UK Students
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What are the Factors of 7500?

The numbers that divide 7500 evenly are known as factors of 7500.

 

A factor of 7500 is a number that divides the number without remainder.

 

The factors of 7500 include 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300, 375, 500, 750, 1500, 2500, 3750, and 7500.

 

Negative factors of 7500: -1, -2, -3, -4, -5, -6, -10, -12, -15, -20, -25, -30, -50, -60, -75, -100, -150, -300, -375, -500, -750, -1500, -2500, -3750, and -7500.

 

Prime factors of 7500: 2, 3, and 5.

 

Prime factorization of 7500: 2² × 3 × 5⁴.

 

The sum of factors of 7500: 1 + 2 + 3 + 4 + 5 + 6 + 10 + 12 + 15 + 20 + 25 + 30 + 50 + 60 + 75 + 100 + 150 + 300 + 375 + 500 + 750 + 1500 + 2500 + 3750 + 7500 = 20160

factors of 7500

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How to Find Factors of 7500?

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 7500. Identifying the numbers which are multiplied to get the number 7500 is the multiplication method.

 

Step 1: Multiply 7500 by 1, 7500 × 1 = 7500.

 

Step 2: Check for other numbers that give 7500 after multiplying

2 × 3750 = 7500

3 × 2500 = 7500

4 × 1875 = 7500

5 × 1500 = 7500

6 × 1250 = 7500

10 × 750 = 7500

15 × 500 = 7500

20 × 375 = 7500

25 × 300 = 7500

30 × 250 = 7500

50 × 150 = 7500

60 × 125 = 7500

75 × 100 = 7500

 

Therefore, the positive factor pairs of 7500 are: (1, 7500), (2, 3750), (3, 2500), (4, 1875), (5, 1500), (6, 1250), (10, 750), (15, 500), (20, 375), (25, 300), (30, 250), (50, 150), (60, 125), and (75, 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 7500 by 1, 7500 ÷ 1 = 7500.

 

Step 2: Continue dividing 7500 by the numbers until the remainder becomes 0.

7500 ÷ 1 = 7500

7500 ÷ 2 = 3750

7500 ÷ 3 = 2500

7500 ÷ 4 = 1875

7500 ÷ 5 = 1500

7500 ÷ 6 = 1250

7500 ÷ 10 = 750

7500 ÷ 15 = 500

7500 ÷ 20 = 375

7500 ÷ 25 = 300

7500 ÷ 30 = 250

7500 ÷ 50 = 150

7500 ÷ 60 = 125

7500 ÷ 75 = 100

 

Therefore, the factors of 7500 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300, 375, 500, 750, 1500, 2500, 3750, and 7500.

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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 7500 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

7500 ÷ 2 = 3750

3750 ÷ 2 = 1875

1875 ÷ 3 = 625

625 ÷ 5 = 125

125 ÷ 5 = 25

25 ÷ 5 = 5

5 ÷ 5 = 1

 

The prime factors of 7500 are 2, 3, and 5.

 

The prime factorization of 7500 is: 2² × 3 × 5⁴.

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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, 7500 is divided by 2 to get 3750.

 

Step 2: Now divide 3750 by 2 to get 1875.

 

Step 3: Then divide 1875 by 3 to get 625.

 

Step 4: Divide 625 by 5 to get 125.

 

Step 5: Divide 125 by 5 to get 25.

 

Step 6: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore.

 

So, the prime factorization of 7500 is: 2² × 3 × 5⁴.

 

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 7500: (1, 7500), (2, 3750), (3, 2500), (4, 1875), (5, 1500), (6, 1250), (10, 750), (15, 500), (20, 375), (25, 300), (30, 250), (50, 150), (60, 125), and (75, 100).

 

Negative factor pairs of 7500: (-1, -7500), (-2, -3750), (-3, -2500), (-4, -1875), (-5, -1500), (-6, -1250), (-10, -750), (-15, -500), (-20, -375), (-25, -300), (-30, -250), (-50, -150), (-60, -125), and (-75, -100).

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Common Mistakes and How to Avoid Them in Factors of 7500

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 word. Always remember to include 1 and the number itself.

 

For example, in factors of 7500, 1 and 7500 is also a factor.

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Factors of 7500 Examples

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Problem 1

There are 10 groups and 7500 candies. How will they divide it equally?

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They will get 750 candies each.

Explanation

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

7500/10 = 750

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Problem 2

A rectangular garden has a length of 25 meters and a total area of 7500 square meters. Find the width?

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300 meters.

Explanation

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

Area = length × width

7500 = 25 × width

To find the value of width, we need to shift 25 to the left side.

7500/25 = width

Width = 300.

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Problem 3

There are 15 boxes and 7500 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 with the boxes.

7500/15 = 500

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Problem 4

In a stadium, there are 7500 spectators, and 50 sections. How many spectators are there in each section?

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There are 150 spectators in each section.

Explanation

Dividing the spectators with the total sections, we will get the number of spectators in each section.

7500/50 = 150

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Problem 5

7500 pages need to be printed and distributed into 25 booklets. How many pages will go into each booklet?

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Each booklet will have 300 pages.

Explanation

Divide total pages with booklets.

7500/25 = 300

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FAQs on Factors of 7500

1.What are the factors of 7500?

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2.Mention the prime factors of 7500.

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3.Is 7500 a multiple of 25?

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4.Mention the factor pairs of 7500?

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5.What is the square of 7500?

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6.How can children in United Kingdom use numbers in everyday life to understand Factors of 7500?

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7.What are some fun ways kids in United Kingdom can practice Factors of 7500 with numbers?

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8.What role do numbers and Factors of 7500 play in helping children in United Kingdom develop problem-solving skills?

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9.How can families in United Kingdom create number-rich environments to improve Factors of 7500 skills?

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Important Glossaries for Factor of 7500

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7500 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300, 375, 500, 750, 1500, 2500, 3750, and 7500.

 

  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 7500.

 

  • 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 7500 are (1, 7500), (2, 3750), etc.

 

  • Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 7500 is 2² × 3 × 5⁴.

 

  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, for 7500, (1, 7500) and (2, 3750) are pairs identified using this method.
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About BrightChamps in United Kingdom

At BrightChamps, numbers are more than just figures—they open doors to endless opportunities! Our mission is to help children across the United Kingdom gain essential math skills, focusing today on Factors of 7500 with special attention to understanding factors—in an engaging, enjoyable, and easy-to-follow way. Whether your child is working out the speed of a roller coaster at Alton Towers, keeping score at a local football match, or managing pocket money to buy the latest gadgets, strong number skills give them confidence in daily life. Our interactive lessons make learning simple and fun. Because children in the UK have varied learning styles, we tailor our approach to suit each learner. From London’s busy streets to Cornwall’s beautiful coasts, BrightChamps brings math to life, making it relatable and exciting throughout the UK. Let’s make factors an enjoyable 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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: She loves to read number jokes and games.

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