100 LearnersLast updated on May 26th, 2025
Factors of 10000
Factors are the numbers that divide any given number evenly without a 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 10000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 10000?
The numbers that divide 10000 evenly are known as factors of 10000.
A factor of 10000 is a number that divides the number without a remainder.
The factors of 10000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 400, 500, 625, 800, 1000, 1250, 2000, 2500, 5000, and 10000.
Negative factors of 10000: -1, -2, -4, -5, -8, -10, -16, -20, -25, -32, -40, -50, -64, -80, -100, -125, -160, -200, -250, -400, -500, -625, -800, -1000, -1250, -2000, -2500, -5000, and -10000.
Prime factors of 10000: 2 and 5.
Prime factorization of 10000: 2^4 × 5^4.
The sum of factors of 10000: 1 + 2 + 4 + 5 + 8 + 10 + 16 + 20 + 25 + 32 + 40 + 50 + 64 + 80 + 100 + 125 + 160 + 200 + 250 + 400 + 500 + 625 + 800 + 1000 + 1250 + 2000 + 2500 + 5000 + 10000 = 25331.
How to Find Factors of 10000?
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
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 10000. Identifying the numbers which are multiplied to get the number 10000 is the multiplication method.
Step 1: Multiply 10000 by 1, 10000 × 1 = 10000.
Step 2: Check for other numbers that give 10000 after multiplying
2 × 5000 = 10000
4 × 2500 = 10000
5 × 2000 = 10000
8 × 1250 = 10000
10 × 1000 = 10000
16 × 625 = 10000
20 × 500 = 10000
25 × 400 = 10000
32 × 312.5 ≠ 10000 (not a factor)
40 × 250 = 10000
50 × 200 = 10000
64 × 156.25 ≠ 10000 (not a factor)
80 × 125 = 10000
100 × 100 = 10000
Therefore, the positive factor pairs of 10000 are: (1, 10000), (2, 5000), (4, 2500), (5, 2000), (8, 1250), (10, 1000), (16, 625), (20, 500), (25, 400), (40, 250), (50, 200), (80, 125), and (100, 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 10000 by 1, 10000 ÷ 1 = 10000.
Step 2: Continue dividing 10000 by the numbers until the remainder becomes 0.
10000 ÷ 1 = 10000
10000 ÷ 2 = 5000
10000 ÷ 4 = 2500
10000 ÷ 5 = 2000
10000 ÷ 8 = 1250
10000 ÷ 10 = 1000
10000 ÷ 16 = 625
10000 ÷ 20 = 500
10000 ÷ 25 = 400
10000 ÷ 40 = 250
10000 ÷ 50 = 200
10000 ÷ 80 = 125
10000 ÷ 100 = 100
Therefore, the factors of 10000 are: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 5000, and 10000.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 10000 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
10000 ÷ 2 = 5000
5000 ÷ 2 = 2500
2500 ÷ 2 = 1250
1250 ÷ 2 = 625
625 ÷ 5 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 10000 are 2 and 5.
The prime factorization of 10000 is: 2^4 × 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, 10000 is divided by 2 to get 5000.
Step 2: Now divide 5000 by 2 to get 2500.
Step 3: Then divide 2500 by 2 to get 1250.
Step 4: Divide 1250 by 2 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.
Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 10000 is: 2^4 × 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 10000: (1, 10000), (2, 5000), (4, 2500), (5, 2000), (8, 1250), (10, 1000), (16, 625), (20, 500), (25, 400), (40, 250), (50, 200), (80, 125), and (100, 100).
Negative factor pairs of 10000: (-1, -10000), (-2, -5000), (-4, -2500), (-5, -2000), (-8, -1250), (-10, -1000), (-16, -625), (-20, -500), (-25, -400), (-40, -250), (-50, -200), (-80, -125), and (-100, -100).
Common Mistakes and How to Avoid Them in Factors of 10000
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 10000, 1 and 10000 are also factors.
Factors of 10000 Examples
Problem 1
There are 10 teams and 10000 units of resources. How will they divide it equally?
They will get 1000 units each.
Explanation
To divide the resources equally, we need to divide the total resources by the number of teams.
10000/10 = 1000
Problem 2
A rectangular park has a length of 500 meters and a total area of 10000 square meters. Find the width.
20 meters.
Explanation
To find the width of the park, we use the formula,
Area = length × width
10000 = 500 × width
To find the value of width, we need to shift 500 to the left side.
10000/500 = width
Width = 20.
Problem 3
There are 2500 boxes and 10000 units of product. How many units will be in each box?
Each box will have 4 units.
Explanation
To find the units in each box, divide the total units by the number of boxes.
10000/2500 = 4
Problem 4
A company has 10000 workers and wants to form 50 teams. How many workers will there be in each team?
There are 200 workers in each team.
Explanation
Dividing the workers by the total number of teams, we will get the number of workers in each team.
10000/50 = 200
Problem 5
10000 books need to be arranged in 25 shelves. How many books will go on each shelf?
Each shelf will have 400 books.
Explanation
Divide total books by the number of shelves.
10000/25 = 400
FAQs on Factors of 10000
1.What are the factors of 10000?
2.Mention the prime factors of 10000.
3.Is 10000 a multiple of 25?
4.Mention the factor pairs of 10000?
5.What is the square of 10000?
6.How can children in Qatar use numbers in everyday life to understand Factors of 10000?
7.What are some fun ways kids in Qatar can practice Factors of 10000 with numbers?
8.What role do numbers and Factors of 10000 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 10000 skills?
Important Glossaries for Factors of 10000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 10000 are 1, 2, 4, 5, 8, 10, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 5 are prime factors of 10000.
- 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 10000 are (1, 10000), (2, 5000), etc.
- Prime factorization: Breaking down a number into the product of its prime factors. For instance, the prime factorization of 10000 is 2^4 × 5^4.
- Division method: A method to find factors by dividing the number by consecutive integers to check if they result in whole numbers.
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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.
Fun Fact
: She loves to read number jokes and games.
