Last updated on May 28th, 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 1584, how they are used in real life, and tips to learn them quickly.
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 can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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: \(24 \times 32 \times 11\).
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
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.
To find how many boxes are needed, divide the total number of cupcakes by the number of cupcakes per box.
1584/18 = 88
A rectangular garden has an area of 1584 square meters. If the length of the garden is 44 meters, find the width.
36 meters.
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.
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.
To find the number of crates needed, divide the total number of gadgets by the number of gadgets per crate.
1584/24 = 66
A school is distributing 1584 notebooks equally among 132 students. How many notebooks will each student receive?
Each student will receive 12 notebooks.
Dividing the total notebooks by the number of students gives the number of notebooks per student.
1584/132 = 12
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.
Divide the total number of books by the number of shelves.
1584/72 = 22
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.
: She loves to read number jokes and games.