101 LearnersLast updated on May 26th, 2025
Factors of 1080
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 1080, how they are used in real life, and tips to learn them quickly.
What are the Factors of 1080?
The numbers that divide 1080 evenly are known as factors of 1080.
A factor of 1080 is a number that divides the number without remainder.
The factors of 1080 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, and 1080.
Negative factors of 1080: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -18, -20, -24, -27, -30, -36, -40, -45, -54, -60, -72, -90, -108, -120, -135, -180, -216, -270, -360, -540, and -1080.
Prime factors of 1080: 2, 3, and 5.
Prime factorization of 1080: \(2^3 \times 3^3 \times 5\).
The sum of factors of 1080: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 18 + 20 + 24 + 27 + 30 + 36 + 40 + 45 + 54 + 60 + 72 + 90 + 108 + 120 + 135 + 180 + 216 + 270 + 360 + 540 + 1080 = 3348
How to Find Factors of 1080?
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 1080. Identifying the numbers which are multiplied to get the number 1080 is the multiplication method.
Step 1: Multiply 1080 by 1, 1080 × 1 = 1080.
Step 2: Check for other numbers that give 1080 after multiplying: -
2 × 540 = 1080
3 × 360 = 1080
4 × 270 = 1080
5 × 216 = 1080
6 × 180 = 1080
9 × 120 = 1080
10 × 108 = 1080
12 × 90 = 1080
15 × 72 = 1080
18 × 60 = 1080
20 × 54 = 1080
24 × 45 = 1080
27 × 40 = 1080
30 × 36 = 1080
Therefore, the positive factor pairs of 1080 are: (1, 1080), (2, 540), (3, 360), (4, 270), (5, 216), (6, 180), (9, 120), (10, 108), (12, 90), (15, 72), (18, 60), (20, 54), (24, 45), (27, 40), and (30, 36).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given number by 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 1080 by 1, 1080 ÷ 1 = 1080.
Step 2: Continue dividing 1080 by the numbers until the remainder becomes 0.
1080 ÷ 1 = 1080
1080 ÷ 2 = 540
1080 ÷ 3 = 360
1080 ÷ 4 = 270
1080 ÷ 5 = 216
1080 ÷ 6 = 180
1080 ÷ 9 = 120
1080 ÷ 10 = 108
1080 ÷ 12 = 90
1080 ÷ 15 = 72
1080 ÷ 18 = 60
1080 ÷ 20 = 54
1080 ÷ 24 = 45
1080 ÷ 27 = 40
1080 ÷ 30 = 36
Therefore, the factors of 1080 are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, and 1080.
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 a factor tree
Using Prime Factorization: In this process, prime factors of 1080 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
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 1080 are 2, 3, and 5.
The prime factorization of 1080 is: \(2^3 \times 3^3 \times 5\).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 1080 is divided by 2 to get 540.
Step 2: Now divide 540 by 2 to get 270.
Step 3: Then divide 270 by 2 to get 135.
Step 4: Divide 135 by 3 to get 45.
Step 5: Divide 45 by 3 to get 15. Step 6: Divide 15 by 3 to get 5.
Here, 5 is the smallest prime number and cannot be divided anymore.
So, the prime factorization of 1080 is: \(2^3 \times 3^3 \times 5\).
Factor Pairs Two numbers that are multiplied to give a specific number are called as factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 1080: (1, 1080), (2, 540), (3, 360), (4, 270), (5, 216), (6, 180), (9, 120), (10, 108), (12, 90), (15, 72), (18, 60), (20, 54), (24, 45), (27, 40), and (30, 36).
Negative factor pairs of 1080: (-1, -1080), (-2, -540), (-3, -360), (-4, -270), (-5, -216), (-6, -180), (-9, -120), (-10, -108), (-12, -90), (-15, -72), (-18, -60), (-20, -54), (-24, -45), (-27, -40), and (-30, -36).
Common Mistakes and How to Avoid Them in Factors of 1080
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 1080, 1 and 1080 are also factors.
Factors of 1080 Examples
Problem 1
There are 9 teachers and 1080 pencils. How will they distribute them equally?
They will get 120 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils by the number of teachers.
1080/9 = 120
Problem 2
A rectangular garden has a length of 15 meters and a total area of 1080 square meters. Find the width.
72 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
1080 = 15 × width
To find the value of width, we need to shift 15 to the left side.
1080/15 = width
Width = 72.
Problem 3
There are 180 boxes and 1080 apples. How many apples will be in each box?
Each box will have 6 apples.
Explanation
To find the apples in each box, divide the total apples by the boxes.
1080/180 = 6
Problem 4
In a school, there are 1080 students and 5 buses. How many students are there in each bus?
There are 216 students in each bus.
Explanation
Dividing the students by the total buses, we will get the number of students in each bus.
1080/5 = 216
Problem 5
1080 books need to be arranged in 9 shelves. How many books will go on each shelf?
Each of the shelves has 120 books.
Explanation
Divide total books by shelves.
1080/9 = 120
FAQs on Factors of 1080
1.What are the factors of 1080?
2.Mention the prime factors of 1080.
3.Is 1080 a multiple of 4?
4.Mention the factor pairs of 1080?
5.What is the square of 1080?
6.How can children in Qatar use numbers in everyday life to understand Factors of 1080?
7.What are some fun ways kids in Qatar can practice Factors of 1080 with numbers?
8.What role do numbers and Factors of 1080 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 1080 skills?
Important Glossaries for Factor of 1080
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1080 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, and 1080.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 1080.
- 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 1080 are (1, 1080), (2, 540), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1080 is \(2^3 \times 3^3 \times 5)
. - Multiples: Numbers that can be divided by another number without a remainder. For example, 1080 is a multiple of 4.
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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.
