126 LearnersLast updated on May 26th, 2025
Factors of 5760
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 5760, how they are used in real life, and tips to learn them quickly.
What are the Factors of 5760?
The numbers that divide 5760 evenly are known as factors of 5760.
A factor of 5760 is a number that divides the number without remainder.
The factors of 5760 include: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 320, 360, 480, 720, 960, 1152, 1440, 1920, 2880, and 5760.
Negative factors of 5760: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -32, -36, -40, -45, -48, -60, -64, -72, -80, -90, -96, -120, -144, -160, -180, -240, -288, -320, -360, -480, -720, -960, -1152, -1440, -1920, -2880, and -5760.
Prime factors of 5760: 2, 3, and 5.
Prime factorization of 5760: 27 × 32 × 5.
The sum of factors of 5760: Calculating this would take adding all the listed factors, which is a large number.
How to Find Factors of 5760?
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 pairs of numbers that are multiplied to give 5760. Identifying the numbers which are multiplied to get the number 5760 is the multiplication method.
Step 1: Multiply 5760 by 1, 5760 × 1 = 5760.
Step 2: Check for other numbers that give 5760 after multiplying. Some examples include:
2 × 2880 = 5760
3 × 1920 = 5760
4 × 1440 = 5760
5 × 1152 = 5760
Therefore, the positive factor pairs of 5760 are: (1, 5760), (2, 2880), (3, 1920), (4, 1440), (5, 1152), etc.
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 as whole numbers as factors. Factors can be calculated by following a simple division method
Step 1: Divide 5760 by 1, 5760 div 1 = 5760.
Step 2: Continue dividing 5760 by the numbers until the remainder becomes 0.
5760 / 1 = 5760
5760 / 2 = 2880
5760 / 3 = 1920
5760 / 4 = 1440
5760 / 5 = 1152
Therefore, the factors of 5760 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 320, 360, 480, 720, 960, 1152, 1440, 1920, 2880, 5760.
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 5760 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5760/ 2 = 2880
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 5760 are 2, 3, and 5.
The prime factorization of 5760 is: 27 × 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, 5760 is divided by 2 to get 2880.
Step 2: Now divide 2880 by 2 to get 1440.
Step 3: Then divide 1440 by 2 to get 720.
Step 4: Divide 720 by 2 to get 360. Continue this process, using 3 and 5 as necessary, to fully factorize 5760. So, the prime factorization of 5760 is: 27 × 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 5760: (1, 5760), (2, 2880), (3, 1920), (4, 1440), (5, 1152), etc.
Negative factor pairs of 5760: (-1, -5760), (-2, -2880), (-3, -1920), (-4, -1440), (-5, -1152), etc.
Common Mistakes and How to Avoid Them in Factors of 5760
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 5760, 1 and 5760 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors; always check whether you have mentioned negative factors.
For example, the factors of 5760 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 5760/1.5 = 3840, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes.
For example, thinking all the factors of 5760 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 5760, but it has other factors like 4, 8, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 5760 as 27 × 32 × 5 and missing all the key factors.
Factors of 5760 Examples
Problem 1
A factory produces 5760 widgets in a month, and they need to be packed in boxes of 240. How many boxes will they fill?
They will fill 24 boxes.
Explanation
To find the number of boxes, we need to divide the total widgets by the capacity of each box.
5760/240 = 24
Problem 2
A rectangular park has an area of 5760 square meters. If one side is 80 meters, what is the length of the other side?
72 meters.
Explanation
To find the length of the other side, we use the formula,
Area = length × width
5760 = 80 × length
To find the value of length, divide the area by the given side.
5760/80 = length
Length = 72.
Problem 3
There are 1152 apples to be distributed equally among some baskets. If each basket can hold 48 apples, how many baskets are needed?
They need 24 baskets.
Explanation
To find the number of baskets, divide the total apples by the number of apples each basket can hold.
1152/48 = 24
Problem 4
A company has 5760 documents to be filed equally in 360 folders. How many documents will go in each folder?
There are 16 documents in each folder.
Explanation
Dividing the documents by the total folders, we will get the number of documents in each folder.
5760/360 = 16
Problem 5
5760 chairs need to be arranged in rows of 180. How many rows will there be?
There will be 32 rows.
Explanation
Divide the total chairs by the number of chairs per row.
5760/180 = 32
FAQs on Factors of 5760
1.What are the factors of 5760?
2.Mention the prime factors of 5760.
3.Is 5760 a multiple of 8?
4.Mention the factor pairs of 5760.
5.What is the square of 5760?
6.How can children in Australia use numbers in everyday life to understand Factors of 5760?
7.What are some fun ways kids in Australia can practice Factors of 5760 with numbers?
8.What role do numbers and Factors of 5760 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 5760 skills?
Important Glossaries for Factor of 5760
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5760 include 1, 2, 3, 4, 5, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 5760.
- 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 5760 are (1, 5760), (2, 2880), etc.
- Prime factorization: Breaking down a number into its prime factors. For example, the prime factorization of 5760 is 27 × 32 × 5.
- Division method: A technique to find factors by dividing the number by integers until a remainder of zero is achieved.
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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
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