100 LearnersLast updated on May 26th, 2025
Factors of 13824
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 13824, how they are used in real life, and tips to learn them quickly.
What are the Factors of 13824?
The numbers that divide 13824 evenly are known as factors of 13824.
A factor of 13824 is a number that divides the number without remainder.
The factors of 13824 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 576, 864, 1152, 1728, 3456, 6912, and 13824.
Negative factors of 13824: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -96, -108, -144, -216, -288, -432, -576, -864, -1152, -1728, -3456, -6912, and -13824.
Prime factors of 13824: 2 and 3.
Prime factorization of 13824: 2^9 × 3^3.
The sum of factors of 13824: TBD (since calculating this sum can be complex without computational assistance).
How to Find Factors of 13824?
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 13824. Identifying the numbers which are multiplied to get the number 13824 is the multiplication method.
Step 1: Multiply 13824 by 1, 13824 × 1 = 13824.
Step 2: Check for other numbers that give 13824 after multiplying:
2 × 6912 = 13824
3 × 4608 = 13824
4 × 3456 = 13824
6 × 2304 = 13824
8 × 1728 = 13824
9 × 1536 = 13824
12 × 1152 = 13824
16 × 864 = 13824
18 × 768 = 13824
24 × 576 = 13824
27 × 512 = 13824
32 × 432 = 13824
36 × 384 = 13824
48 × 288 = 13824
54 × 256 = 13824
72 × 192 = 13824
96 × 144 = 13824
Therefore, the positive factor pairs of 13824 include: (1, 13824), (2, 6912), (3, 4608), 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 13824 by 1, 13824 ÷ 1 = 13824.
Step 2: Continue dividing 13824 by the numbers until the remainder becomes 0.
13824 ÷ 1 = 13824
13824 ÷ 2 = 6912
13824 ÷ 3 = 4608
13824 ÷ 4 = 3456
13824 ÷ 6 = 2304
13824 ÷ 8 = 1728
13824 ÷ 9 = 1536
13824 ÷ 12 = 1152
13824 ÷ 16 = 864
13824 ÷ 18 = 768
13824 ÷ 24 = 576
13824 ÷ 27 = 512
13824 ÷ 32 = 432
13824 ÷ 36 = 384
13824 ÷ 48 = 288
13824 ÷ 54 = 256
13824 ÷ 72 = 192
13824 ÷ 96 = 144
Therefore, the factors of 13824 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 576, 864, 1152, 1728, 3456, 6912, 13824.
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 13824 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
13824 ÷ 2 = 6912
6912 ÷ 2 = 3456
3456 ÷ 2 = 1728
1728 ÷ 2 = 864
864 ÷ 2 = 432
432 ÷ 2 = 216
216 ÷ 2 = 108
108 ÷ 2 = 54
54 ÷ 3 = 18
18 ÷ 3 = 6
6 ÷ 3 = 2
The prime factors of 13824 are 2 and 3.
The prime factorization of 13824 is: 2^9 × 3^3.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 13824 is divided by 2 to get 6912.
Step 2: Now divide 6912 by 2 to get 3456.
Step 3: Then divide 3456 by 2 to get 1728.
Step 4: Continue this process until you reach a prime number.
Eventually, you will reach 1. The prime factorization of 13824 is: 2^9 × 3^3.
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 13824: (1, 13824), (2, 6912), (3, 4608), (4, 3456), (6, 2304), (8, 1728), (9, 1536), (12, 1152), (16, 864), (18, 768), (24, 576), (27, 512), (32, 432), (36, 384), (48, 288), (54, 256), (72, 192), (96, 144).
Negative factor pairs of 13824: (-1, -13824), (-2, -6912), (-3, -4608), (-4, -3456), (-6, -2304), (-8, -1728), (-9, -1536), (-12, -1152), (-16, -864), (-18, -768), (-24, -576), (-27, -512), (-32, -432), (-36, -384), (-48, -288), (-54, -256), (-72, -192), (-96, -144).
Common Mistakes and How to Avoid Them in Factors of 13824
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 13824, 1 and 13824 are also factors.
Factors of 13824 Examples
Problem 1
A factory produces 13824 widgets in a day. If they pack the widgets into boxes containing 144 each, how many boxes are needed?
96 boxes are needed.
Explanation
To find the number of boxes needed, divide the total widgets by the number of widgets per box.
13824/144 = 96
Problem 2
A farmer has a field area of 13824 square meters. If the width of the field is 72 meters, what is the length?
The length of the field is 192 meters.
Explanation
To find the length of the field, use the formula:
Area = length × width
13824 = length × 72
Length = 13824/72 = 192
Problem 3
There are 2880 bottles to be packed in crates, and each crate holds 18 bottles. How many crates will be used?
160 crates will be used.
Explanation
To find the number of crates needed, divide the total bottles by the number of bottles per crate.
2880/18 = 160
Problem 4
A school has 13824 students, and they are divided into 432 classes. How many students are in each class?
There are 32 students in each class.
Explanation
Dividing the total students by the number of classes gives the number of students per class.
13824/432 = 32
Problem 5
A library has 13824 books to be arranged in shelves with 576 books each. How many shelves are required?
24 shelves are required.
Explanation
Divide the total number of books by the number of books per shelf.
13824/576 = 24
FAQs on Factors of 13824
1.What are the factors of 13824?
2.Mention the prime factors of 13824.
3.Is 13824 a multiple of 8?
4.Mention the factor pairs of 13824?
5.What is the square of 13824?
6.How can children in India use numbers in everyday life to understand Factors of 13824?
7.What are some fun ways kids in India can practice Factors of 13824 with numbers?
8.What role do numbers and Factors of 13824 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 13824 skills?
Important Glossaries for Factor of 13824
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 13824 are 1, 2, 3, 4, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 13824.
- 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 13824 are (1, 13824), (2, 6912), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, 13824 can be expressed as 2^9 × 3^3.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number. For example, using 2 × 6912 to find factors of 13824.
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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.
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