113 LearnersLast updated on May 26th, 2025
Factors of 5184
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 5184, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 5184?
The numbers that divide 5184 evenly are known as factors of 5184.
A factor of 5184 is a number that divides the number without remainder.
The factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1296, 2592, and 5184.
Negative factors of 5184: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -81, -96, -108, -144, -162, -216, -324, -432, -648, -864, -1296, -2592, and -5184.
Prime factors of 5184: 2 and 3.
Prime factorization of 5184: 26 × 34.
The sum of factors of 5184: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 81 + 96 + 108 + 144 + 162 + 216 + 324 + 432 + 648 + 864 + 1296 + 2592 + 5184 = 15876
How to Find Factors of 5184?
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 5184. Identifying the numbers which are multiplied to get the number 5184 is the multiplication method.
Step 1: Multiply 5184 by 1, 5184 × 1 = 5184.
Step 2: Check for other numbers that give 5184 after multiplying
2 × 2592 = 5184
3 × 1728 = 5184
4 × 1296 = 5184
6 × 864 = 5184
8 × 648 = 5184
9 × 576 = 5184
12 × 432 = 5184
16 × 324 = 5184
18 × 288 = 5184
24 × 216 = 5184
27 × 192 = 5184
32 × 162 = 5184
36 × 144 = 5184
48 × 108 = 5184
54 × 96 = 5184
72 × 72 = 5184
Therefore, the positive factor pairs of 5184 are: (1, 5184), (2, 2592), (3, 1728), (4, 1296), (6, 864), (8, 648), (9, 576), (12, 432), (16, 324), (18, 288), (24, 216), (27, 192), (32, 162), (36, 144), (48, 108), (54, 96), and (72, 72).
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 a simple division method
Step 1: Divide 5184 by 1, 5184 ÷ 1 = 5184.
Step 2: Continue dividing 5184 by the numbers until the remainder becomes 0.
5184 ÷ 1 = 5184
5184 ÷ 2 = 2592
5184 ÷ 3 = 1728
5184 ÷ 4 = 1296
5184 ÷ 6 = 864
5184 ÷ 8 = 648
5184 ÷ 9 = 576
5184 ÷ 12 = 432
5184 ÷ 16 = 324
5184 ÷ 18 = 288
5184 ÷ 24 = 216
5184 ÷ 27 = 192
5184 ÷ 32 = 162
5184 ÷ 36 = 144
5184 ÷ 48 = 108
5184 ÷ 54 = 96
5184 ÷ 72 = 72
Therefore, the factors of 5184 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1296, 2592, and 5184.
Prime Factors and Prime Factorization
The factors can be found by dividing them with 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 5184 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5184 ÷ 2 = 2592
2592 ÷ 2 = 1296
1296 ÷ 2 = 648
648 ÷ 2 = 324
324 ÷ 2 = 162
162 ÷ 2 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 5184 are 2 and 3.
The prime factorization of 5184 is: 26 × 34.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 5184 is divided by 2 to get 2592.
Step 2: Now divide 2592 by 2 to get 1296.
Step 3: Then divide 1296 by 2 to get 648.
Step 4: Divide 648 by 2 to get 324.
Step 5: Divide 324 by 2 to get 162.
Step 6: Divide 162 by 2 to get 81.
Step 7: Divide 81 by 3 to get 27.
Step 8: Divide 27 by 3 to get 9.
Step 9: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore. So, the prime factorization of 5184 is: 26 × 34.
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 5184: (1, 5184), (2, 2592), (3, 1728), (4, 1296), (6, 864), (8, 648), (9, 576), (12, 432), (16, 324), (18, 288), (24, 216), (27, 192), (32, 162), (36, 144), (48, 108), (54, 96), and (72, 72).
Negative factor pairs of 5184: (-1, -5184), (-2, -2592), (-3, -1728), (-4, -1296), (-6, -864), (-8, -648), (-9, -576), (-12, -432), (-16, -324), (-18, -288), (-24, -216), (-27, -192), (-32, -162), (-36, -144), (-48, -108), (-54, -96), and (-72, -72).
Common Mistakes and How to Avoid Them in Factors of 5184
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 5184, 1 and 5184 are also factors.
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 5184 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 5184/1.5 = 3456, 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 5184 are prime numbers.
For example, 2 and 3 are the prime factors of 5184, but it has other factors like 4, 9.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 5184 as 26 × 34 and missing all the key factors.
Factors of 5184 Examples
Problem 1
There are 72 children and 5184 candies. How will they divide it equally?
They will get 72 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of children.
5184/72 = 72
Problem 2
A garden is rectangular, the length of the garden is 54 meters and the total area is 5184 square meters. Find the width?
96 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
5184 = 54 × width
To find the value of width, we need to shift 54 to the left side.
5184/54 = width
Width = 96.
Problem 3
There are 324 boxes and 5184 marbles. How many marbles will be in each box?
Each box will have 16 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes.
5184/324 = 16
Problem 4
In a school, there are 5184 students, and 432 classes. How many students are there in each class?
There are 12 students in each class.
Explanation
Dividing the students by the total classes, we will get the number of students in each class.
5184/432 = 12
Problem 5
5184 books need to be arranged in 108 shelves. How many books will go on each shelf?
Each of the shelves has 48 books.
Explanation
Divide the total books by shelves.
5184/108 = 48
FAQs on Factors of 5184
1.What are the factors of 5184?
2.Mention the prime factors of 5184.
3.Is 5184 a multiple of 8?
4.Mention the factor pairs of 5184?
5.What is the square of 5184?
6.How can children in Qatar use numbers in everyday life to understand Factors of 5184?
7.What are some fun ways kids in Qatar can practice Factors of 5184 with numbers?
8.What role do numbers and Factors of 5184 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 5184 skills?
Important Glossaries for Factors of 5184
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 324, 432, 648, 864, 1296, 2592, and 5184.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 5184.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 5184 is 26 × 34.
- 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 5184 are (1, 5184), (2, 2592), etc.
- Division method: A technique to find factors by dividing the given number by whole numbers until the remainder is zero.
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About BrightChamps in Qatar
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.
