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Last updated on May 28th, 2025

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Factors of 1584

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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 1584, how they are used in real life, and tips to learn them quickly.

Factors of 1584 for US Students
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What are the Factors of 1584?

The numbers that divide 1584 evenly are known as factors of 1584.

 

A factor of 1584 is a number that divides the number without remainder.

 

The factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 44, 48, 72, 88, 96, 132, 144, 176, 264, 288, 396, 528, 792, and 1584.

 

Negative factors of 1584: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -32, -36, -44, -48, -72, -88, -96, -132, -144, -176, -264, -288, -396, -528, -792, and -1584.

 

Prime factors of 1584: 2, 3, and 11.

 

Prime factorization of 1584: 24 × 32 × 11.

 

The sum of factors of 1584: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 32 + 36 + 44 + 48 + 72 + 88 + 96 + 132 + 144 + 176 + 264 + 288 + 396 + 528 + 792 + 1584 = 5184

Factors of 1584

 

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How to Find Factors of 1584?

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
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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 1584. Identifying the numbers which are multiplied to get the number 1584 is the multiplication method.

 

Step 1: Multiply 1584 by 1, 1584 × 1 = 1584.

 

Step 2: Check for other numbers that give 1584 after multiplying

 

2 × 792 = 1584

3 × 528 = 1584

4 × 396 = 1584

6 × 264 = 1584

8 × 198 = 1584

9 × 176 = 1584

12 × 132 = 1584

16 × 99 = 1584

18 × 88 = 1584

24 × 66 = 1584

32 × 49.5 = 1584

(Note: This is not a factor due to the fraction)

36 × 44 = 1584

 

Therefore, the positive factor pairs of 1584 are: (1, 1584), (2, 792), (3, 528), (4, 396), (6, 264), (8, 198), (9, 176), (12, 132), (16, 99), (18, 88), (24, 66), (36, 44).

 

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 simple division method -

 

Step 1: Divide 1584 by 1, 1584 ÷ 1 = 1584.

 

Step 2: Continue dividing 1584 by the numbers until the remainder becomes 0.

 

1584 ÷ 1 = 1584

1584 ÷ 2 = 792

1584 ÷ 3 = 528

1584 ÷ 4 = 396

1584 ÷ 6 = 264

1584 ÷ 8 = 198

1584 ÷ 9 = 176

1584 ÷ 12 = 132

1584 ÷ 16 = 99

1584 ÷ 18 = 88

1584 ÷ 24 = 66

1584 ÷ 36 = 44

 

Therefore, the factors of 1584 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 44, 66, 88, 99, 132, 176, 198, 264, 396, 528, 792, 1584.

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Prime Factors and Prime Factorization

The factors can be found by dividing it with a 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 1584 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.

 

1584 ÷ 2 = 792

792 ÷ 2 = 396

396 ÷ 2 = 198

198 ÷ 2 = 99

99 ÷ 3 = 33

33 ÷ 3 = 11

11 ÷ 11 = 1

 

The prime factors of 1584 are 2, 3, and 11.

 

The prime factorization of 1584 is: \(24 \times 32 \times 11\).

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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, 1584 is divided by 2 to get 792.

 

Step 2: Now divide 792 by 2 to get 396.

 

Step 3: Then divide 396 by 2 to get 198.

 

Step 4: Divide 198 by 2 to get 99.

 

Step 5: Divide 99 by 3 to get 33.

 

Step 6: Divide 33 by 3 to get 11.

 

Step 7: Finally, divide 11 by 11 to get 1. So, the prime factorization of 1584 is: \(24 \times 32 \times 11\).

 

Factor Pairs Two numbers that are multiplied to give a specific number are called as factor pairs.

Both positive and negative factors constitute factor pairs.

 

Positive factor pairs of 1584: (1, 1584), (2, 792), (3, 528), (4, 396), (6, 264), (8, 198), (9, 176), (12, 132), (16, 99), (18, 88), (24, 66), (36, 44).

 

Negative factor pairs of 1584: (-1, -1584), (-2, -792), (-3, -528), (-4, -396), (-6, -264), (-8, -198), (-9, -176), (-12, -132), (-16, -99), (-18, -88), (-24, -66), (-36, -44).

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Common Mistakes and How to Avoid Them in Factors of 1584

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 1584, 1 and 1584 is also a factor.

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Factors of 1584 Examples

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Problem 1

A baker has 1584 cupcakes. If they want to arrange them into boxes with 18 cupcakes each, how many boxes will they need?

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They will need 88 boxes.

Explanation

To find how many boxes are needed, divide the total number of cupcakes by the number of cupcakes per box.

 

1584/18 = 88

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Problem 2

A rectangular garden has an area of 1584 square meters. If the length of the garden is 44 meters, find the width.

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36 meters.

Explanation

To find the width of the garden, use the formula,

 

Area = length × width

 

1584 = 44 × width

 

To find the value of width, divide the area by the length.

 

1584/44 = width

 

Width = 36.

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Problem 3

A factory produces 1584 gadgets, and they need to be packed into crates of 24 gadgets each. How many crates will be used?

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66 crates will be used.

Explanation

To find the number of crates needed, divide the total number of gadgets by the number of gadgets per crate.

 

1584/24 = 66

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Problem 4

A school is distributing 1584 notebooks equally among 132 students. How many notebooks will each student receive?

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Each student will receive 12 notebooks.

Explanation

Dividing the total notebooks by the number of students gives the number of notebooks per student.

 

1584/132 = 12

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Problem 5

A library has 1584 books, and they are to be placed equally on 72 shelves. How many books will go on each shelf?

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Each shelf will have 22 books.

Explanation

Divide the total number of books by the number of shelves.

 

1584/72 = 22

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FAQs on Factors of 1584

1.What are the factors of 1584?

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2.Mention the prime factors of 1584.

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3.Is 1584 a multiple of 11?

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4.Mention the factor pairs of 1584.

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5.What is the square of 1584?

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6.How can children in United States use numbers in everyday life to understand Factors of 1584?

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7.What are some fun ways kids in United States can practice Factors of 1584 with numbers?

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8.What role do numbers and Factors of 1584 play in helping children in United States develop problem-solving skills?

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9.How can families in United States create number-rich environments to improve Factors of 1584 skills?

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Important Glossaries for Factor of 1584

  • Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, etc.

     
  • Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 1584.

     
  • 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 1584 are (1, 1584), (2, 792), etc.

     
  • Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 1584 is \(24 \times 32 \times 11\).

     
  • Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the given number.
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About BrightChamps in United States

At BrightChamps, we believe numbers are more than symbols—they unlock a world full of possibilities! Our goal is to support kids throughout the United States in mastering key math skills, such as today’s Factors of 1584, with a special emphasis on understanding factors—in a way that’s engaging, fun, and easy to grasp. Whether your child is calculating the speed of a roller coaster at Disney World, tracking scores at a Little League baseball game, or budgeting their allowance to buy cool gadgets, understanding numbers builds their confidence for everyday tasks. Our hands-on lessons make learning enjoyable and straightforward. Since kids in the USA learn in unique ways, we customize our methods to match each child’s style. From the busy streets of New York City to the sunny beaches of California, BrightChamps makes math come alive, bringing it closer to children everywhere. Let’s turn factors into an exciting part of every child’s math adventure!
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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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