102 LearnersLast updated on May 26th, 2025
Factors of 14400
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 14400, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 14400?
The numbers that divide 14400 evenly are known as factors of 14400.
A factor of 14400 is a number that divides the number without remainder.
The factors of 14400 are numerous, including 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 160, 180, 200, 225, 240, 288, 300, 360, 400, 450, 480, 600, 720, 900, 1200, 1440, 1800, 2400, 3600, 4800, 7200, and 14400.
Negative factors of 14400: Corresponding negative numbers.
Prime factors of 14400: 2, 3, and 5.
Prime factorization of 14400: 2^6 × 3^2 × 5^2.
The sum of factors of 14400: A large number resulting from adding all factors of 14400.
How to Find Factors of 14400?
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 14400. Identifying the numbers which are multiplied to get the number 14400 is the multiplication method.
Step 1: Multiply 14400 by 1, 14400 × 1 = 14400.
Step 2: Check for other numbers that give 14400 after multiplying
2 × 7200 = 14400
3 × 4800 = 14400
4 × 3600 = 14400
5 × 2880 = 14400
6 × 2400 = 14400 …and so on.
Therefore, the positive factor pairs of 14400 are too numerous to list fully here.
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 14400 by 1, 14400 ÷ 1 = 14400.
Step 2: Continue dividing 14400 by the numbers until the remainder becomes 0.
14400 ÷ 1 = 14400
14400 ÷ 2 = 7200
14400 ÷ 3 = 4800
14400 ÷ 4 = 3600
14400 ÷ 5 = 2880
14400 ÷ 6 = 2400 …and so forth.
Therefore, the factors of 14400 are numerous, including 1, 2, 3, 4, 5, 6, 8, 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 14400 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
14400 ÷ 2 = 7200
7200 ÷ 2 = 3600
3600 ÷ 2 = 1800
1800 ÷ 2 = 900
900 ÷ 2 = 450
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 14400 are 2, 3, and 5.
The prime factorization of 14400 is: 2^6 × 3^2 × 5^2.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 14400 is divided by 2 to get 7200.
Step 2: Now divide 7200 by 2 to get 3600.
Step 3: Then divide 3600 by 2 to get 1800.
Step 4: Divide 1800 by 2 to get 900.
Step 5: Divide 900 by 2 to get 450.
Step 6: Divide 450 by 2 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 14400 is: 2^6 × 3^2 × 5^2.
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 14400: (1, 14400), (2, 7200), (3, 4800), (4, 3600), (5, 2880), (6, 2400), etc.
Negative factor pairs of 14400: (-1, -14400), (-2, -7200), (-3, -4800), (-4, -3600), (-5, -2880), (-6, -2400), etc.
Common Mistakes and How to Avoid Them in Factors of 14400
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 word. Always remember to include 1 and the number itself.
For example, in factors of 14400, 1 and 14400 are also factors.
Factors of 14400 Examples
Problem 1
There are 24 students and 14400 candies. How will they divide it equally?
They will get 600 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
14400/24 = 600
Problem 2
A garden is rectangular, the length of the garden is 60 meters, and the total area is 14400 square meters. Find the width?
240 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
14400 = 60 × width
To find the value of width, we need to shift 60 to the left side.
14400/60 = width
Width = 240.
Problem 3
There are 144 bags and 14400 marbles. How many marbles will be in each bag?
Each bag will have 100 marbles.
Explanation
To find the marbles in each bag, divide the total marbles by the bags.
14400/144 = 100
Problem 4
In a factory, there are 14400 products, and 360 boxes. How many products are there in each box?
There are 40 products in each box.
Explanation
Dividing the products with the total boxes, we will get the number of products in each box.
14400/360 = 40
Problem 5
14400 books need to be arranged in 180 shelves. How many books will go on each shelf?
Each of the shelves has 80 books.
Explanation
Divide total books with shelves.
14400/180 = 80
FAQs on Factors of 14400
1.What are the factors of 14400?
2.Mention the prime factors of 14400.
3.Is 14400 a multiple of 12?
4.Mention the factor pairs of 14400?
5.What is the square root of 14400?
6.How can children in Bahrain use numbers in everyday life to understand Factors of 14400?
7.What are some fun ways kids in Bahrain can practice Factors of 14400 with numbers?
8.What role do numbers and Factors of 14400 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve Factors of 14400 skills?
Important Glossaries for Factor of 14400
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 14400 include 1, 2, 3, 4, and many more.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 14400.
- 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 14400 are (1, 14400), (2, 7200), etc.
- Prime factorization: The expression of a number as a product of its prime factors. For example, the prime factorization of 14400 is 2^6 × 3^2 × 5^2.
- Multiplication method: A technique to find factors by identifying pairs of numbers that multiply to a given number.
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About BrightChamps in Bahrain
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.
