119 LearnersLast updated on May 26th, 2025
Factors of 21600
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.
What are the Factors of 21600?
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.
How to Find Factors of 21600?
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 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.
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 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.
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 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.
Factor Tree
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.
Common Mistakes and How to Avoid Them in Factors of 21600
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
Individuals 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 21600, 1 and 21600 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 21600 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
People might sometimes add fractions also as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 21600/1.5 = 14400, 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 21600 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 21600, but it has other factors like 4, 10.
Mistake 5
Mistake in Factorization
Individuals might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 21600 properly into 25 × 33 × 52 and missing key factors.
Factors of 21600 Examples
Problem 1
There are 15 workers and 21600 bricks. How will they distribute them equally?
They will get 1440 bricks each.
Explanation
To distribute the bricks equally, we need to divide the total bricks by the number of workers.
21600/15 = 1440
Problem 2
A rectangular pool has a width of 12 meters and a total area of 21600 square meters. Find the length?
1800 meters.
Explanation
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.
Problem 3
There are 54 crates and 21600 apples. How many apples will be in each crate?
Each crate will have 400 apples.
Explanation
To find the apples in each crate, divide the total apples by the crates.
21600/54 = 400
Problem 4
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.
Explanation
Dividing the pencils by the total groups, we will get the number of pencils in each group.
21600/45 = 480
Problem 5
21600 books need to be arranged in 360 shelves. How many books will go on each shelf?
Each of the shelves has 60 books.
Explanation
Divide total books by shelves.
21600/360 = 60
FAQs on Factors of 21600
1.What are the factors of 21600?
2.Mention the prime factors of 21600.
3.Is 21600 a multiple of 9?
4.Mention the factor pairs of 21600?
5.What is the square root of 21600?
6.How can children in Vietnam use numbers in everyday life to understand Factors of 21600?
7.What are some fun ways kids in Vietnam can practice Factors of 21600 with numbers?
8.What role do numbers and Factors of 21600 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Factors of 21600 skills?
Important Glossaries for Factors of 21600
- Factors: Numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 21600 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 21600.
- 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 21600 include (1, 21600), (2, 10800), etc.
- Multiples: A multiple of a number is the product of that number and an integer. For example, 21600 is a multiple of 9.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 21600 is 2^5 × 3^3 × 5^2.
Explore More numbers
About BrightChamps in Vietnam
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.
