Factors of 14400
2026-02-28 08:29 Diff
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Last updated on December 12, 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 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.

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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: 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.

Download Worksheets

Problem 1

There are 24 students and 14400 candies. How will they divide it equally?

Okay, lets begin

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

Well explained 👍

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?

Okay, lets begin

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.

Well explained 👍

Problem 3

There are 144 bags and 14400 marbles. How many marbles will be in each bag?

Okay, lets begin

Each bag will have 100 marbles.

Explanation

To find the marbles in each bag, divide the total marbles by the bags.

14400/144 = 100

Well explained 👍

Problem 4

In a factory, there are 14400 products, and 360 boxes. How many products are there in each box?

Okay, lets begin

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

Well explained 👍

Problem 5

14400 books need to be arranged in 180 shelves. How many books will go on each shelf?

Okay, lets begin

Each of the shelves has 80 books.

Explanation

Divide total books with shelves.

14400/180 = 80

Well explained 👍

FAQs on Factors of 14400

1.What are the factors of 14400?

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 are the factors of 14400.

2.Mention the prime factors of 14400.

The prime factors of 14400 are 2^6 × 3^2 × 5^2.

3.Is 14400 a multiple of 12?

4.Mention the factor pairs of 14400?

(1, 14400), (2, 7200), (3, 4800), (4, 3600), (5, 2880), (6, 2400), etc., are the factor pairs of 14400.

5.What is the square root of 14400?

The square root of 14400 is 120.

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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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.