Last updated on May 26th, 2025
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.
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.
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To find the number of boxes, we need to divide the total widgets by the capacity of each box.
5760/240 = 24
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.
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.
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.
To find the number of baskets, divide the total apples by the number of apples each basket can hold.
1152/48 = 24
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.
Dividing the documents by the total folders, we will get the number of documents in each folder.
5760/360 = 16
5760 chairs need to be arranged in rows of 180. How many rows will there be?
There will be 32 rows.
Divide the total chairs by the number of chairs per row.
5760/180 = 32
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.
: She loves to read number jokes and games.