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Last updated on May 26th, 2025

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Factors of 1728

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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 1728, how they are used in real life, and tips to learn them quickly.

Factors of 1728 for Bahraini Students
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What are the Factors of 1728?

The numbers that divide 1728 evenly are known as factors of 1728.

 

A factor of 1728 is a number that divides the number without a remainder.

 

The factors of 1728 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, and 1728.

 

Negative factors of 1728: -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, and -1728.

 

Prime factors of 1728: 2 and 3.

 

Prime factorization of 1728: 26 × 33.

 

The sum of factors of 1728: 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 + 1728 = 5084.

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How to Find Factors of 1728?

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
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Finding Factors Using Multiplication

To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 1728. Identifying the numbers which are multiplied to get the number 1728 is the multiplication method.

 

Step 1: Multiply 1728 by 1, 1728 × 1 = 1728.

 

Step 2: Check for other numbers that give 1728 after multiplying:

 

2 × 864 = 1728

3 × 576 = 1728

4 × 432 = 1728

6 × 288 = 1728

8 × 216 = 1728

9 × 192 = 1728

12 × 144 = 1728

16 × 108 = 1728

18 × 96 = 1728

24 × 72 = 1728

27 × 64 = 1728

32 × 54 = 1728

36 × 48 = 1728

 

Therefore, the positive factor pairs of 1728 are: (1, 1728), (2, 864), (3, 576), (4, 432), (6, 288), (8, 216), (9, 192), (12, 144), (16, 108), (18, 96), (24, 72), (27, 64), (32, 54), (36, 48).

 

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 as whole numbers as factors. Factors can be calculated by following a simple division method

 

Step 1: Divide 1728 by 1, 1728 ÷ 1 = 1728.

 

Step 2: Continue dividing 1728 by the numbers until the remainder becomes 0.

 

1728 ÷ 1 = 1728

1728 ÷ 2 = 864

1728 ÷ 3 = 576

1728 ÷ 4 = 432

1728 ÷ 6 = 288

1728 ÷ 8 = 216

 

Therefore, the factors of 1728 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, 1728.

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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 a factor tree

 

Using Prime Factorization: In this process, prime factors of 1728 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.

 

1728 ÷ 2 = 864

864 ÷ 2 = 432

432 ÷ 2 = 216

216 ÷ 2 = 108

108 ÷ 2 = 54

54 ÷ 2 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

 

The prime factors of 1728 are 2 and 3.

 

The prime factorization of 1728 is: 26 × 33.

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Factor Tree

The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:

 

Step 1: Firstly, 1728 is divided by 2 to get 864.

 

Step 2: Now divide 864 by 2 to get 432.

 

Step 3: Then divide 432 by 2 to get 216.

 

Step 4: Divide 216 by 2 to get 108.

 

Step 5: Divide 108 by 2 to get 54.

 

Step 6: Divide 54 by 2 to get 27.

 

Step 7: Divide 27 by 3 to get 9.

 

Step 8: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 1728 is: 26 × 33.

 

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 1728: (1, 1728), (2, 864), (3, 576), (4, 432), (6, 288), (8, 216), (9, 192), (12, 144), (16, 108), (18, 96), (24, 72), (27, 64), (32, 54), (36, 48).

 

Negative factor pairs of 1728: (-1, -1728), (-2, -864), (-3, -576), (-4, -432), (-6, -288), (-8, -216), (-9, -192), (-12, -144), (-16, -108), (-18, -96), (-24, -72), (-27, -64), (-32, -54), (-36, -48).

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Common Mistakes and How to Avoid Them in Factors of 1728

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

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Forgetting the number itself and 1 is a factor

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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 1728, 1 and 1728 are also factors.

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Factors of 1728 Examples

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Problem 1

There are 6 teams and 1728 coins. How will they divide it equally?

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They will get 288 coins each.

Explanation

To divide the coins equally, we need to divide the total coins by the number of teams.

 

1728/6 = 288

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Problem 2

A storage box is cubic, with a volume of 1728 cubic centimeters. If the length of one edge is 12 cm, find the area of one face of the cube.

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144 square centimeters.

Explanation

To find the area of one face of the cube, use the formula:

 

Area = edge × edge

 

Since the edge length is 12 cm,

 

Area = 12 × 12 = 144

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Problem 3

There are 9 pallets and 1728 bricks. How many bricks will be on each pallet?

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Each pallet will have 192 bricks.

Explanation

To find the bricks on each pallet, divide the total bricks by the number of pallets.

 

1728/9 = 192

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Problem 4

A class has 1728 students, and they need to be divided into 16 groups. How many students are there in each group?

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There are 108 students in each group.

Explanation

Dividing the students by the total groups, we will get the number of students in each group.

 

1728/16 = 108

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Problem 5

1728 apples need to be packed into 18 crates. How many apples will go in each crate?

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Each crate will have 96 apples.

Explanation

Divide the total apples by the crates.

 

1728/18 = 96

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FAQs on Factors of 1728

1.What are the factors of 1728?

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2.Mention the prime factors of 1728.

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3.Is 1728 a multiple of 12?

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4.Mention the factor pairs of 1728?

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5.What is the cube root of 1728?

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6.How can children in Bahrain use numbers in everyday life to understand Factors of 1728?

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7.What are some fun ways kids in Bahrain can practice Factors of 1728 with numbers?

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8.What role do numbers and Factors of 1728 play in helping children in Bahrain develop problem-solving skills?

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9.How can families in Bahrain create number-rich environments to improve Factors of 1728 skills?

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Important Glossaries for Factors of 1728

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1728 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, and 1728.
     
  • Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 1728.
     
  • 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 1728 are (1, 1728), (2, 864), etc.
     
  • Prime factorization: The process of expressing a number as a multiplication of its prime factors. For example, the prime factorization of 1728 is 26 × 33.
     
  • Division method: A method to find factors by dividing a number by integers to see if the result is a whole number without a remainder. For example, when dividing 1728 by 6, the result is 288, which is a factor.
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About BrightChamps in Bahrain

At BrightChamps, numbers are more than just digits—they unlock countless opportunities! Our goal is to help kids all over Bahrain build essential math skills, focusing today on Factors of 1728 with a special focus on factors—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Wahooo! Waterpark, keeping track of local football scores, or managing their allowance for gadgets, mastering numbers boosts everyday confidence. Our interactive lessons make learning simple and enjoyable. Since kids in Bahrain learn in various ways, we adapt lessons to fit each learner. From Manama’s lively city to peaceful beaches, BrightChamps brings math to life all over Bahrain. Let’s make factors a fun part of every child’s math journey!
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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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Fun Fact

: She loves to read number jokes and games.

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