101 LearnersLast updated on May 26th, 2025
Factors of 2880
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 2880, how they are used in real life, and tips to learn them quickly.
What are the Factors of 2880?
The numbers that divide 2880 evenly are known as factors of 2880.
A factor of 2880 is a number that divides the number without remainder.
The factors of 2880 include a variety of numbers, such as 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 320, 360, 480, 576, 720, 960, 1440, and 2880.
Negative factors of 2880: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -32, -36, -40, -45, -48, -60, -72, -80, -90, -96, -120, -144, -160, -180, -240, -288, -320, -360, -480, -576, -720, -960, -1440, and -2880.
Prime factors of 2880: 2, 3, and 5.
Prime factorization of 2880: 26 × 32 × 5.
The sum of factors of 2880: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 45 + 48 + 60 + 72 + 80 + 90 + 96 + 120 + 144 + 160 + 180 + 240 + 288 + 320 + 360 + 480 + 576 + 720 + 960 + 1440 + 2880 = 8064
How to Find Factors of 2880?
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 2880. Identifying the numbers which are multiplied to get the number 2880 is the multiplication method.
Step 1: Multiply 2880 by 1, 2880 × 1 = 2880.
Step 2: Check for other numbers that give 2880 after multiplying:
2 × 1440 = 2880
3 × 960 = 2880
4 × 720 = 2880
5 × 576 = 2880
6 × 480 = 2880
8 × 360 = 2880
9 × 320 = 2880
10 × 288 = 2880
12 × 240 = 2880
15 × 192 = 2880
16 × 180 = 2880
18 × 160 = 2880
20 × 144 = 2880
24 × 120 = 2880
30 × 96 = 2880
32 × 90 = 2880
36 × 80 = 2880
40 × 72 = 2880
45 × 64 = 2880
48 × 60 = 2880
Therefore, the positive factor pairs of 2880 include: (1, 2880), (2, 1440), (3, 960), (4, 720), (5, 576), (6, 480), (8, 360), (9, 320), (10, 288), (12, 240), (15, 192), (16, 180), (18, 160), (20, 144), (24, 120), (30, 96), (32, 90), (36, 80), (40, 72), (45, 64), and (48, 60). For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 2880 by 1, 2880 ÷ 1 = 2880.
Step 2: Continue dividing 2880 by the numbers until the remainder becomes 0.
2880 ÷ 1 = 2880
2880 ÷ 2 = 1440
2880 ÷ 3 = 960
2880 ÷ 4 = 720
2880 ÷ 5 = 576
2880 ÷ 6 = 480
2880 ÷ 8 = 360
2880 ÷ 9 = 320
2880 ÷ 10 = 288
2880 ÷ 12 = 240
2880 ÷ 15 = 192
2880 ÷ 16 = 180
2880 ÷ 18 = 160
2880 ÷ 20 = 144
2880 ÷ 24 = 120
2880 ÷ 30 = 96
2880 ÷ 32 = 90
2880 ÷ 36 = 80
2880 ÷ 40 = 72
2880 ÷ 45 = 64
2880 ÷ 48 = 60
Therefore, the factors of 2880 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 320, 360, 480, 576, 720, 960, 1440, and 2880.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 2880 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
2880 ÷ 2 = 1440
1440 ÷ 2 = 720
720 ÷ 2 = 360
360 ÷ 2 = 180
180 ÷ 2 = 90
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 2880 are 2, 3, and 5.
The prime factorization of 2880 is: 26 × 32 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show:
Step 1: Firstly, 2880 is divided by 2 to get 1440.
Step 2: Now divide 1440 by 2 to get 720.
Step 3: Then divide 720 by 2 to get 360.
Step 4: Divide 360 by 2 to get 180.
Step 5: Divide 180 by 2 to get 90.
Step 6: Divide 90 by 2 to get 45.
Step 7: Divide 45 by 3 to get 15.
Step 8: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 2880 is: 26 × 32 × 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 2880: (1, 2880), (2, 1440), (3, 960), (4, 720), (5, 576), (6, 480), (8, 360), (9, 320), (10, 288), (12, 240), (15, 192), (16, 180), (18, 160), (20, 144), (24, 120), (30, 96), (32, 90), (36, 80), (40, 72), (45, 64), and (48, 60).
Negative factor pairs of 2880: (-1, -2880), (-2, -1440), (-3, -960), (-4, -720), (-5, -576), (-6, -480), (-8, -360), (-9, -320), (-10, -288), (-12, -240), (-15, -192), (-16, -180), (-18, -160), (-20, -144), (-24, -120), (-30, -96), (-32, -90), (-36, -80), (-40, -72), (-45, -64), and (-48, -60).
Common Mistakes and How to Avoid Them in Factors of 2880
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 2880, 1 and 2880 are also factors.
Factors of 2880 Examples
Problem 1
There are 144 people and 2880 balloons. How will they divide it equally?
They will get 20 balloons each.
Explanation
To divide the balloons equally, we need to divide the total balloons by the number of people.
2880/144 = 20
Problem 2
A garden is rectangular, the length of the garden is 60 meters and the total area is 2880 square meters. Find the width?
48 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
2880 = 60 × width
To find the value of width, we need to shift 60 to the left side.
2880/60 = width
Width = 48
Problem 3
There are 160 bags and 2880 candies. How many candies will be in each bag?
Each bag will have 18 candies.
Explanation
To find the candies in each bag, divide the total candies by the bags.
2880/160 = 18
Problem 4
In a class, there are 2880 students, and 360 groups. How many students are there in each group?
There are 8 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
2880/360 = 8
Problem 5
2880 books need to be arranged in 60 shelves. How many books will go on each shelf?
Each of the shelves has 48 books.
Explanation
Divide total books by shelves.
2880/60 = 48
FAQs on Factors of 2880
1.What are the factors of 2880?
2.Mention the prime factors of 2880.
3.Is 2880 a multiple of 6?
4.Mention the factor pairs of 2880?
5.What is the square of 2880?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of 2880?
7.What are some fun ways kids in Saudi Arabia can practice Factors of 2880 with numbers?
8.What role do numbers and Factors of 2880 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of 2880 skills?
Important Glossaries for Factors of 2880
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 2880 include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 2880.
- 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 2880 are (1, 2880), (2, 1440), etc.
- Prime factorization: The process of breaking down a number into its prime factors. For 2880, it is 26 × 32 × 5.
- Multiplication method: A method to find 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.
Fun Fact
: She loves to read number jokes and games.
