101 LearnersLast updated on May 26th, 2025
Factors of 15000
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 15000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 15000?
The numbers that divide 15000 evenly are known as factors of 15000.
A factor of 15000 is a number that divides the number without remainder.
The factors of 15000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 7500, and 15000.
Negative factors of 15000: -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -16, -20, -24, -25, -30, -40, -48, -50, -60, -75, -80, -100, -120, -150, -200, -240, -250, -300, -375, -400, -500, -600, -750, -1000, -1200, -1500, -1875, -2000, -2500, -3000, -3750, -5000, -7500, and -15000.
Prime factors of 15000: 2, 3, and 5.
Prime factorization of 15000: \(2^3 \times 3 \times 5^4\).
The sum of factors of 15000: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 16 + 20 + 24 + 25 + 30 + 40 + 48 + 50 + 60 + 75 + 80 + 100 + 120 + 150 + 200 + 240 + 250 + 300 + 375 + 400 + 500 + 600 + 750 + 1000 + 1200 + 1500 + 1875 + 2000 + 2500 + 3000 + 3750 + 5000 + 7500 + 15000 = 46596
How to Find Factors of 15000?
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 15000. Identifying the numbers which are multiplied to get the number 15000 is the multiplication method.
Step 1: Multiply 15000 by 1, 15000 × 1 = 15000.
Step 2: Check for other numbers that give 15000 after multiplying
2 × 7500 = 15000
3 × 5000 = 15000
5 × 3000 = 15000
6 × 2500 = 15000
8 × 1875 = 15000
10 × 1500 = 15000
12 × 1250 = 15000
15 × 1000 = 15000
20 × 750 = 15000
25 × 600 = 15000
30 × 500 = 15000
40 × 375 = 15000
50 × 300 = 15000
60 × 250 = 15000
75 × 200 = 15000
80 × 187.5 = 15000
100 × 150 = 15000
120 × 125 = 15000
150 × 100 = 15000
200 × 75 = 15000
240 × 62.5 = 15000
250 × 60 = 15000
300 × 50 = 15000
375 × 40 = 15000
400 × 37.5 = 15000
500 × 30 = 15000
600 × 25 = 15000
750 × 20 = 15000
1000 × 15 = 15000
1200 × 12.5 = 15000
1500 × 10 = 15000
1875 × 8 = 15000
2000 × 7.5 = 15000
2500 × 6 = 15000
3000 × 5 = 15000
3750 × 4 = 15000
5000 × 3 = 15000
7500 × 2 = 15000
15000 × 1 = 15000
Therefore, the positive factor pairs of 15000 include: (1, 15000), (2, 7500), (3, 5000), (4, 3750), (5, 3000), (6, 2500), (8, 1875), (10, 1500), (12, 1250), (15, 1000), (20, 750), (25, 600), (30, 500), (40, 375), (50, 300), (60, 250), (75, 200), (100, 150), (120, 125).
All these factor pairs result in 15000.
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 15000 by 1, 15000 ÷ 1 = 15000.
Step 2: Continue dividing 15000 by the numbers until the remainder becomes 0.
15000 ÷ 1 = 15000
15000 ÷ 2 = 7500
15000 ÷ 3 = 5000
15000 ÷ 4 = 3750
15000 ÷ 5 = 3000
15000 ÷ 6 = 2500
15000 ÷ 8 = 1875
15000 ÷ 10 = 1500
15000 ÷ 12 = 1250
15000 ÷ 15 = 1000
15000 ÷ 20 = 750
15000 ÷ 25 = 600
15000 ÷ 30 = 500
15000 ÷ 40 = 375
15000 ÷ 50 = 300
15000 ÷ 60 = 250
15000 ÷ 75 = 200
15000 ÷ 100 = 150
15000 ÷ 120 = 125
Therefore, the factors of 15000 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 7500, and 15000.
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 15000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
15000 ÷ 2 = 7500
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 15000 are 2, 3, and 5.
The prime factorization of 15000 is: \(2^3 \times 3 \times 5^4\).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 15000 is divided by 2 to get 7500.
Step 2: Now divide 7500 by 2 to get 3750.
Step 3: Then divide 3750 by 2 to get 1875.
Step 4: Divide 1875 by 3 to get 625.
Step 5: Divide 625 by 5 to get 125.
Step 6: Divide 125 by 5 to get 25.
Step 7: Divide 25 by 5 to get 5.
Step 8: Divide 5 by 5 to get 1.
Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 15000 is: \(2^3 \times 3 \times 5^4\).
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 15000: (1, 15000), (2, 7500), (3, 5000), (4, 3750), (5, 3000), (6, 2500), (8, 1875), (10, 1500), (12, 1250), (15, 1000), (20, 750), (25, 600), (30, 500), (40, 375), (50, 300), (60, 250), (75, 200), (100, 150), (120, 125).
Negative factor pairs of 15000: (-1, -15000), (-2, -7500), (-3, -5000), (-4, -3750), (-5, -3000), (-6, -2500), (-8, -1875), (-10, -1500), (-12, -1250), (-15, -1000), (-20, -750), (-25, -600), (-30, -500), (-40, -375), (-50, -300), (-60, -250), (-75, -200), (-100, -150), (-120, -125).
Common Mistakes and How to Avoid Them in Factors of 15000
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 number. Always remember to include 1 and the number itself.
For example, in factors of 15000, 1 and 15000 are also factors.
Factors of 15000 Examples
Problem 1
There are 300 students and 15000 candies. How will they divide it equally?
They will get 50 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
15000/300 = 50
Problem 2
A rectangular garden has a length of 100 meters and a total area of 15000 square meters. Find the width.
150 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
15000 = 100 × width
To find the value of width, we need to shift 100 to the left side.
15000/100 = width
Width = 150.
Problem 3
There are 150 boxes and 15000 apples. How many apples will be in each box?
Each box will have 100 apples.
Explanation
To find the apples in each box, divide the total apples with the boxes.
15000/150 = 100
Problem 4
In a school, there are 200 students, and each student has 75 pencils. What is the total number of pencils?
15000 pencils.
Explanation
Multiplying the students with pencils per student, we get the total number of pencils.
200 × 75 = 15000
Problem 5
15000 pages need to be printed and compiled into 150 books. How many pages will each book have?
Each book will have 100 pages.
Explanation
Divide the total number of pages by the number of books.
15000/150 = 100
FAQs on Factors of 15000
1.What are the factors of 15000?
2.Mention the prime factors of 15000.
3.Is 15000 a multiple of 5?
4.Mention the factor pairs of 15000?
5.What is the square of 15000?
6.How can children in Thailand use numbers in everyday life to understand Factors of 15000?
7.What are some fun ways kids in Thailand can practice Factors of 15000 with numbers?
8.What role do numbers and Factors of 15000 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors of 15000 skills?
Important Glossaries for Factors of 15000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 15000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 250, 300, 375, 400, 500, 600, 750, 1000, 1200, 1500, 1875, 2000, 2500, 3000, 3750, 5000, 7500, and 15000.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 15000.
- 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 15000 are (1, 15000), (2, 7500), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. The prime factorization of 15000 is \(2^3 \times 3 \times 5^4\).
- Multiplication method: A method to find factors by identifying number pairs that multiply to the given number. For example, 5 and 3000 are factors of 15000 because 5 × 3000 = 15000.
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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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