100 LearnersLast updated on May 26th, 2025
Factors of 10800
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 10800, how they are used in real life, and tips to learn them quickly.
What are the Factors of 10800?
The numbers that divide 10800 evenly are known as factors of 10800.
A factor of 10800 is a number that divides the number without remainder.
The factors of 10800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 54, 60, 72, 75, 80, 90, 100, 108, 120, 135, 144, 150, 180, 200, 216, 225, 240, 270, 300, 360, 400, 450, 540, 600, 675, 720, 900, 1080, 1200, 1350, 1800, 2160, 2700, 3600, 5400, and 10800.
Negative factors of 10800: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -27, -30, -36, -40, -45, -48, -54, -60, -72, -75, -80, -90, -100, -108, -120, -135, -144, -150, -180, -200, -216, -225, -240, -270, -300, -360, -400, -450, -540, -600, -675, -720, -900, -1080, -1200, -1350, -1800, -2160, -2700, -3600, -5400, and -10800.
Prime factors of 10800: 2, 3, and 5.
Prime factorization of 10800: 2^4 × 3^3 × 5^2.
The sum of factors of 10800: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 25 + 27 + 30 + 36 + 40 + 45 + 48 + 54 + 60 + 72 + 75 + 80 + 90 + 100 + 108 + 120 + 135 + 144 + 150 + 180 + 200 + 216 + 225 + 240 + 270 + 300 + 360 + 400 + 450 + 540 + 600 + 675 + 720 + 900 + 1080 + 1200 + 1350 + 1800 + 2160 + 2700 + 3600 + 5400 + 10800 = 39312
How to Find Factors of 10800?
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 10800. Identifying the numbers which are multiplied to get the number 10800 is the multiplication method.
Step 1: Multiply 10800 by 1, 10800 × 1 = 10800.
Step 2: Check for other numbers that give 10800 after multiplying
2 × 5400 = 10800
3 × 3600 = 10800
4 × 2700 = 10800
5 × 2160 = 10800
6 × 1800 = 10800
8 × 1350 = 10800
9 × 1200 = 10800
10 × 1080 = 10800
12 × 900 = 10800
15 × 720 = 10800
18 × 600 = 10800
20 × 540 = 10800
24 × 450 = 10800
25 × 432 = 10800
27 × 400 = 10800
30 × 360 = 10800
36 × 300 = 10800
40 × 270 = 10800
45 × 240 = 10800
48 × 225 = 10800
54 × 200 = 10800
60 × 180 = 10800
72 × 150 = 10800
75 × 144 = 10800
80 × 135 = 10800
90 × 120 = 10800
100 × 108 = 10800
Therefore, the positive factor pairs of 10800 are: (1, 10800), (2, 5400), (3, 3600), (4, 2700), (5, 2160), (6, 1800), (8, 1350), (9, 1200), (10, 1080), (12, 900), (15, 720), (18, 600), (20, 540), (24, 450), (25, 432), (27, 400), (30, 360), (36, 300), (40, 270), (45, 240), (48, 225), (54, 200), (60, 180), (72, 150), (75, 144), (80, 135), (90, 120), (100, 108).
All these factor pairs result in 10800.
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 10800 by 1, 10800 ÷ 1 = 10800.
Step 2: Continue dividing 10800 by the numbers until the remainder becomes 0.
10800 ÷ 1 = 10800
10800 ÷ 2 = 5400
10800 ÷ 3 = 3600
10800 ÷ 4 = 2700
10800 ÷ 5 = 2160
10800 ÷ 6 = 1800
10800 ÷ 8 = 1350
10800 ÷ 9 = 1200
10800 ÷ 10 = 1080
10800 ÷ 12 = 900
10800 ÷ 15 = 720
10800 ÷ 18 = 600
10800 ÷ 20 = 540
10800 ÷ 24 = 450
10800 ÷ 25 = 432
10800 ÷ 27 = 400
10800 ÷ 30 = 360
10800 ÷ 36 = 300
10800 ÷ 40 = 270
10800 ÷ 45 = 240
10800 ÷ 48 = 225
10800 ÷ 54 = 200
10800 ÷ 60 = 180
10800 ÷ 72 = 150
10800 ÷ 75 = 144
10800 ÷ 80 = 135
10800 ÷ 90 = 120
10800 ÷ 100 = 108
Therefore, the factors of 10800 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 54, 60, 72, 75, 80, 90, 100, 108, 120, 135, 144, 150, 180, 200, 216, 225, 240, 270, 300, 360, 400, 450, 540, 600, 675, 720, 900, 1080, 1200, 1350, 1800, 2160, 2700, 3600, 5400, and 10800.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 10800 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
10800 ÷ 2 = 5400
5400 ÷ 2 = 2700
2700 ÷ 2 = 1350
1350 ÷ 2 = 675
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 10800 are 2, 3, and 5.
The prime factorization of 10800 is: 2^4 × 3^3 × 5^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 10800 is divided by 2 to get 5400.
Step 2: Now divide 5400 by 2 to get 2700.
Step 3: Then divide 2700 by 2 to get 1350.
Step 4: Divide 1350 by 2 to get 675.
Step 5: Divide 675 by 3 to get 225.
Step 6: Divide 225 by 3 to get 75.
Step 7: Divide 75 by 3 to get 25.
Step 8: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number that cannot be divided anymore. So, the prime factorization of 10800 is: 2^4 × 3^3 × 5^2.
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 10800: (1, 10800), (2, 5400), (3, 3600), (4, 2700), (5, 2160), (6, 1800), (8, 1350), (9, 1200), (10, 1080), (12, 900), (15, 720), (18, 600), (20, 540), (24, 450), (25, 432), (27, 400), (30, 360), (36, 300), (40, 270), (45, 240), (48, 225), (54, 200), (60, 180), (72, 150), (75, 144), (80, 135), (90, 120), (100, 108).
Negative factor pairs of 10800: (-1, -10800), (-2, -5400), (-3, -3600), (-4, -2700), (-5, -2160), (-6, -1800), (-8, -1350), (-9, -1200), (-10, -1080), (-12, -900), (-15, -720), (-18, -600), (-20, -540), (-24, -450), (-25, -432), (-27, -400), (-30, -360), (-36, -300), (-40, -270), (-45, -240), (-48, -225), (-54, -200), (-60, -180), (-72, -150), (-75, -144), (-80, -135), (-90, -120), (-100, -108).
Common Mistakes and How to Avoid Them in Factors of 10800
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 10800, 1 and 10800 are also factors.
Factors of 10800 Examples
Problem 1
There are 108 students and 10800 candies. How will they divide it equally?
They will get 100 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of students.
10800/108 = 100
Problem 2
A garden is rectangular, the length of the garden is 90 meters, and the total area is 10800 square meters. Find the width?
120 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
10800 = 90 × width
To find the value of width, we need to shift 90 to the left side.
10800/90 = width
Width = 120.
Problem 3
There are 450 baskets and 10800 apples. How many apples will be in each basket?
Each basket will have 24 apples.
Explanation
To find the apples in each basket, divide the total apples by the baskets.
10800/450 = 24
Problem 4
In a company, there are 360 employees, and each team has 10800 tasks. How many tasks does each employee handle?
Each employee handles 30 tasks.
Explanation
Dividing the tasks with the total employees, we will get the number of tasks each employee handles.
10800/360 = 30
Problem 5
10800 books need to be arranged in 60 shelves. How many books will go on each shelf?
Each shelf has 180 books.
Explanation
Divide total books by shelves.
10800/60 = 180
FAQs on Factors of 10800
1.What are the factors of 10800?
2.Mention the prime factors of 10800.
3.Is 10800 a multiple of 4?
4.Mention the factor pairs of 10800?
5.What is the square of 10800?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 10800?
7.What are some fun ways kids in United Kingdom can practice Factors of 10800 with numbers?
8.What role do numbers and Factors of 10800 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 10800 skills?
Important Glossaries for Factor of 10800
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 10800 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 54, 60, 72, 75, 80, 90, 100, 108, 120, 135, 144, 150, 180, 200, 216, 225, 240, 270, 300, 360, 400, 450, 540, 600, 675, 720, 900, 1080, 1200, 1350, 1800, 2160, 2700, 3600, 5400, and 10800.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 10800.
- 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 10800 are (1, 10800), (2, 5400), etc.
- Prime factorization: The process of expressing a number as a product of its prime numbers. For example, the prime factorization of 10800 is 2^4 × 3^3 × 5^2.
- Multiplication method: A method of finding factors by identifying pairs of numbers that multiply to give the original number.
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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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