137 LearnersLast updated on May 28th, 2025
Factors of 1584
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.
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
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
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.
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.
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: \(24 \times 32 \times 11\).
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).
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
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 1584, 1 and 1584 is also a factor.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 1584 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 1584/1.5 = 1056, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not only just primes. For example, thinking all the factors of 1584 are prime numbers.
For example, 2, 3, and 11 are the prime factors of 1584, but it has other factors like 4, 8, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 1584 as \(24 \times 32 \times 11\) and missing all the key factors.
Factors of 1584 Examples
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?
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
Problem 2
A rectangular garden has an area of 1584 square meters. If the length of the garden is 44 meters, find the width.
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.
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?
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
Problem 4
A school is distributing 1584 notebooks equally among 132 students. How many notebooks will each student receive?
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
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?
Each shelf will have 22 books.
Explanation
Divide the total number of books by the number of shelves.
1584/72 = 22
FAQs on Factors of 1584
1.What are the factors of 1584?
2.Mention the prime factors of 1584.
3.Is 1584 a multiple of 11?
4.Mention the factor pairs of 1584.
5.What is the square of 1584?
6.How can children in United States use numbers in everyday life to understand Factors of 1584?
7.What are some fun ways kids in United States can practice Factors of 1584 with numbers?
8.What role do numbers and Factors of 1584 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 1584 skills?
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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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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