147 LearnersLast updated on May 26th, 2025
Factors of 7500
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.
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 × 5â´.
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
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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
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.
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.
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 × 5â´.
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 × 5â´.
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).
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
Forgetting the number itself and 1 is a factor
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.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 7500 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 7500/1.5 is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 7500 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 7500, but it has other factors like 10, 25.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 7500 as 2² × 3 × 5â´ and missing all the key factors.
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Factors of 7500 Examples
Problem 1
There are 10 groups and 7500 candies. How will they divide it equally?
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
Problem 2
A rectangular garden has a length of 25 meters and a total area of 7500 square meters. Find the width?
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.
Problem 3
There are 15 boxes and 7500 marbles. How many marbles will be in each box?
Each box will have 500 marbles.
Explanation
To find the marbles in each box, divide the total marbles with the boxes.
7500/15 = 500
Problem 4
In a stadium, there are 7500 spectators, and 50 sections. How many spectators are there in each section?
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
Problem 5
7500 pages need to be printed and distributed into 25 booklets. How many pages will go into each booklet?
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?
2.Mention the prime factors of 7500.
3.Is 7500 a multiple of 25?
4.Mention the factor pairs of 7500?
5.What is the square of 7500?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 7500?
7.What are some fun ways kids in United Kingdom can practice Factors of 7500 with numbers?
8.What role do numbers and Factors of 7500 play in helping children in United Kingdom develop problem-solving skills?
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 × 5â´.
- 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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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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