Last updated on May 26th, 2025
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 21600, how they are used in real life, and tips to learn them quickly.
The numbers that divide 21600 evenly are known as factors of 21600. A factor of 21600 is a number that divides the number without a remainder.
The factors of 21600 include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 75, 80, 90, 100, 108, 120, 135, 144, 150, 160, 180, 200, 216, 225, 240, 270, 288, 300, 360, 400, 432, 450, 480, 540, 600, 720, 900, 1080, 1200, 1350, 1440, 1800, 2160, 2700, 3600, 4320, 5400, 7200, 10800, and 21600.
Negative factors of 21600: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -25, -27, -30, -32, -36, -40, -45, -48, -54, -60, -72, -75, -80, -90, -100, -108, -120, -135, -144, -150, -160, -180, -200, -216, -225, -240, -270, -288, -300, -360, -400, -432, -450, -480, -540, -600, -720, -900, -1080, -1200, -1350, -1440, -1800, -2160, -2700, -3600, -4320, -5400, -7200, -10800, and -21600.
Prime factors of 21600: 2, 3, and 5.
Prime factorization of 21600: 25 × 33 × 52.
The sum of factors of 21600 is quite large and is typically calculated using a formula for the sum of divisors.
Factors can be found using different methods. Mentioned below are some commonly used methods:
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 21600. Identifying the numbers that are multiplied to get the number 21600 is the multiplication method.
Step 1: Multiply 21600 by 1, 21600 × 1 = 21600.
Step 2: Check for other numbers that give 21600 after multiplying.
Example pairs: 2 × 10800 = 21600
3 × 7200 = 21600
4 × 5400 = 21600
5 × 4320 = 21600
Therefore, the positive factor pairs of 21600 include (1, 21600), (2, 10800), (3, 7200), (4, 5400), (5, 4320), and others. 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 21600 by 1, 21600 ÷ 1 = 21600.
Step 2: Continue dividing 21600 by the numbers until the remainder becomes 0.
Examples: 21600 ÷ 1 = 21600
21600 ÷ 2 = 10800
21600 ÷ 3 = 7200
21600 ÷ 4 = 5400
21600 ÷ 5 = 4320
Therefore, the factors of 21600 are many and include 1, 2, 3, 4, 5, and many more.
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 21600 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
Example: 21600 ÷ 2 = 10800
10800 ÷ 2 = 5400
5400 ÷ 2 = 2700
2700 ÷ 2 = 1350
1350 ÷ 2 = 675
675 ÷ 3 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 21600 are 2, 3, and 5.
The prime factorization of 21600 is: 25 × 33 × 52.
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 21600 is divided by 2 to get 10800.
Step 2: Now divide 10800 by 2 to get 5400.
Step 3: Then divide 5400 by 2 to get 2700.
Step 4: Divide 2700 by 2 to get 1350.
Step 5: Divide 1350 by 2 to get 675.
Step 6: Divide 675 by 3 to get 225.
Step 7: Divide 225 by 3 to get 75.
Step 8: Divide 75 by 3 to get 25.
Step 9: Divide 25 by 5 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 21600 is: 25 × 33 × 52.
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 21600 include (1, 21600), (2, 10800), (3, 7200), (4, 5400), (5, 4320), etc.
Negative factor pairs of 21600 include (-1, -21600), (-2, -10800), (-3, -7200), (-4, -5400), (-5, -4320), 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.
There are 15 workers and 21600 bricks. How will they distribute them equally?
They will get 1440 bricks each.
To distribute the bricks equally, we need to divide the total bricks by the number of workers.
21600/15 = 1440
A rectangular pool has a width of 12 meters and a total area of 21600 square meters. Find the length?
1800 meters.
To find the length of the pool, we use the formula,
Area = length × width
21600 = length × 12
To find the value of length, we need to shift 12 to the left side.
21600/12 = length
Length = 1800.
There are 54 crates and 21600 apples. How many apples will be in each crate?
Each crate will have 400 apples.
To find the apples in each crate, divide the total apples by the crates.
21600/54 = 400
In a class, there are 21600 pencils, and 45 groups. How many pencils are there in each group?
There are 480 pencils in each group.
Dividing the pencils by the total groups, we will get the number of pencils in each group.
21600/45 = 480
21600 books need to be arranged in 360 shelves. How many books will go on each shelf?
Each of the shelves has 60 books.
Divide total books by shelves.
21600/360 = 60
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.