101 LearnersLast updated on May 26th, 2025
Factors of 2160
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 2160, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2160?
The numbers that divide 2160 evenly are known as factors of 2160.
A factor of 2160 is a number that divides the number without remainder.
The factors of 2160 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 240, 270, 360, 432, 540, 720, 1080, and 2160.
Negative factors of 2160: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -27, -30, -36, -40, -45, -54, -60, -72, -90, -108, -120, -135, -180, -216, -240, -270, -360, -432, -540, -720, -1080, and -2160.
Prime factors of 2160: 2, 3, and 5.
Prime factorization of 2160: 2^4 × 3^3 × 5.
The sum of factors of 2160: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 27 + 30 + 36 + 40 + 45 + 54 + 60 + 72 + 90 + 108 + 120 + 135 + 180 + 216 + 240 + 270 + 360 + 432 + 540 + 720 + 1080 + 2160 = 7440
How to Find Factors of 2160?
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 2160. Identifying the numbers which are multiplied to get the number 2160 is the multiplication method.
Step 1: Multiply 2160 by 1, 2160 × 1 = 2160.
Step 2: Check for other numbers that give 2160 after multiplying:
2 × 1080 = 2160
3 × 720 = 2160
4 × 540 = 2160
5 × 432 = 2160
6 × 360 = 2160
8 × 270 = 2160
9 × 240 = 2160
10 × 216 = 2160
12 × 180 = 2160
15 × 144 = 2160
18 × 120 = 2160
20 × 108 = 2160
24 × 90 = 2160
27 × 80 = 2160
30 × 72 = 2160
36 × 60 = 2160
40 × 54 = 2160
45 × 48 = 2160
Therefore, the positive factor pairs of 2160 are: (1, 2160), (2, 1080), (3, 720), (4, 540), (5, 432), (6, 360), (8, 270), (9, 240), (10, 216), (12, 180), (15, 144), (18, 120), (20, 108), (24, 90), (27, 80), (30, 72), (36, 60), (40, 54), (45, 48).
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 in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 2160 by 1, 2160 ÷ 1 = 2160.
Step 2: Continue dividing 2160 by the numbers until the remainder becomes 0:
2160 ÷ 1 = 2160
2160 ÷ 2 = 1080
2160 ÷ 3 = 720
2160 ÷ 4 = 540
2160 ÷ 5 = 432
2160 ÷ 6 = 360
2160 ÷ 8 = 270
2160 ÷ 9 = 240
2160 ÷ 10 = 216
2160 ÷ 12 = 180
2160 ÷ 15 = 144
2160 ÷ 18 = 120
2160 ÷ 20 = 108
2160 ÷ 24 = 90
2160 ÷ 27 = 80
2160 ÷ 30 = 72
2160 ÷ 36 = 60
2160 ÷ 40 = 54
2160 ÷ 45 = 48
Therefore, the factors of 2160 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 240, 270, 360, 432, 540, 720, 1080, 2160.
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 2160 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
2160 ÷ 2 = 1080
1080 ÷ 2 = 540
540 ÷ 2 = 270
270 ÷ 2 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 2160 are 2, 3, and 5.
The prime factorization of 2160 is: 2^4 × 3^3 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 2160 is divided by 2 to get 1080.
Step 2: Now divide 1080 by 2 to get 540.
Step 3: Then divide 540 by 2 to get 270.
Step 4: Divide 270 by 2 to get 135.
Step 5: Divide 135 by 3 to get 45.
Step 6: Divide 45 by 3 to get 15.
Step 7: Divide 15 by 3 to get 5.
Here, 5 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 2160 is: 2^4 × 3^3 × 5.
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 2160: (1, 2160), (2, 1080), (3, 720), (4, 540), (5, 432), (6, 360), (8, 270), (9, 240), (10, 216), (12, 180), (15, 144), (18, 120), (20, 108), (24, 90), (27, 80), (30, 72), (36, 60), (40, 54), (45, 48).
Negative factor pairs of 2160: (-1, -2160), (-2, -1080), (-3, -720), (-4, -540), (-5, -432), (-6, -360), (-8, -270), (-9, -240), (-10, -216), (-12, -180), (-15, -144), (-18, -120), (-20, -108), (-24, -90), (-27, -80), (-30, -72), (-36, -60), (-40, -54), (-45, -48).
Common Mistakes and How to Avoid Them in Factors of 2160
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 2160, 1 and 2160 are also factors.
Factors of 2160 Examples
Problem 1
There are 9 friends and 2160 candies. How will they divide it equally?
They will get 240 candies each.
Explanation
To divide the candies equally, we need to divide the total candies with the number of friends.
2160/9 = 240
Problem 2
A garden is rectangular, the length of the garden is 24 meters and the total area is 2160 square meters. Find the width?
90 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2160 = 24 × width
To find the value of width, we need to shift 24 to the left side.
2160/24 = width
Width = 90.
Problem 3
There are 36 boxes and 2160 books. How many books will be in each box?
Each box will have 60 books.
Explanation
To find the books in each box, divide the total books with the boxes.
2160/36 = 60
Problem 4
In a factory, there are 2160 workers, and 72 teams. How many workers are there in each team?
There are 30 workers in each team.
Explanation
Dividing the workers with the total teams, we will get the number of workers in each team.
2160/72 = 30
Problem 5
2160 apples need to be packed in 54 crates. How many apples will go in each crate?
Each of the crates will have 40 apples.
Explanation
Divide the total apples with crates.
2160/54 = 40
FAQs on Factors of 2160
1.What are the factors of 2160?
2.Mention the prime factors of 2160.
3.Is 2160 a multiple of 9?
4.Mention the factor pairs of 2160?
5.What is the square of 2160?
6.How can children in Australia use numbers in everyday life to understand Factors of 2160?
7.What are some fun ways kids in Australia can practice Factors of 2160 with numbers?
8.What role do numbers and Factors of 2160 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 2160 skills?
Important Glossaries for Factors of 2160
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2160 are 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 2160.
- 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 2160 are (1, 2160), (2, 1080), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to get the original number.
- Division method: A method to find factors by dividing the number with whole numbers until the remainder is zero.
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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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