123 LearnersLast updated on May 26th, 2025
Factors of 5832
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 5832, how they are used in real life, and some tips to learn them quickly.
What are the Factors of 5832?
The numbers that divide 5832 evenly are known as factors of 5832.
A factor of 5832 is a number that divides the number without remainder.
The factors of 5832 include 1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 36, 54, 81, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, and 5832.
Negative factors of 5832: -1, -2, -3, -4, -6, -8, -9, -12, -18, -27, -36, -54, -81, -108, -162, -216, -324, -486, -648, -972, -1458, -1944, -2916, and -5832.
Prime factors of 5832: 2 and 3.
Prime factorization of 5832: 23 × 36.
The sum of factors of 5832: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 216 + 324 + 486 + 648 + 972 + 1458 + 1944 + 2916 + 5832 = 17424
How to Find Factors of 5832?
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
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that multiply to give 5832. Identifying the numbers which are multiplied to get the number 5832 is the multiplication method.
Step 1: Multiply 5832 by 1, 5832 × 1 = 5832.
Step 2: Check for other numbers that give 5832 after multiplying:
2 × 2916 = 5832
3 × 1944 = 5832
4 × 1458 = 5832
6 × 972 = 5832
9 × 648 = 5832
12 × 486 = 5832
18 × 324 = 5832
27 × 216 = 5832
36 × 162 = 5832
54 × 108 = 5832
81 × 72 = 5832
Therefore, the positive factor pairs of 5832 are: (1, 5832), (2, 2916), (3, 1944), (4, 1458), (6, 972), (8, 729), (9, 648), (12, 486), (18, 324), (27, 216), (36, 162), (54, 108), and (81, 72).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with 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 5832 by 1, 5832 ÷ 1 = 5832.
Step 2: Continue dividing 5832 by the numbers until the remainder becomes 0.
5832 ÷ 1 = 5832
5832 ÷ 2 = 2916
5832 ÷ 3 = 1944
5832 ÷ 4 = 1458
5832 ÷ 6 = 972
5832 ÷ 8 = 729
5832 ÷ 9 = 648
5832 ÷ 12 = 486
5832 ÷ 18 = 324
5832 ÷ 27 = 216
5832 ÷ 36 = 162
5832 ÷ 54 = 108
5832 ÷ 81 = 72
Therefore, the factors of 5832 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 36, 54, 81, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, and 5832.
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 5832 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
5832 ÷ 2 = 2916
2916 ÷ 2 = 1458
1458 ÷ 2 = 729
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of 5832 are 2 and 3.
The prime factorization of 5832 is: 23 × 36.
Factor Tree
The factor tree is a graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 5832 is divided by 2 to get 2916.
Step 2: Now divide 2916 by 2 to get 1458.
Step 3: Then divide 1458 by 2 to get 729.
Step 4: Divide 729 by 3 to get 243.
Step 5: Divide 243 by 3 to get 81.
Step 6: Divide 81 by 3 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, that cannot be divided anymore. So, the prime factorization of 5832 is: 23 × 36.
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 5832: (1, 5832), (2, 2916), (3, 1944), (4, 1458), (6, 972), (8, 729), (9, 648), (12, 486), (18, 324), (27, 216), (36, 162), (54, 108), (72, 81).
Negative factor pairs of 5832: (-1, -5832), (-2, -2916), (-3, -1944), (-4, -1458), (-6, -972), (-8, -729), (-9, -648), (-12, -486), (-18, -324), (-27, -216), (-36, -162), (-54, -108), (-72, -81).
Common Mistakes and How to Avoid Them in Factors of 5832
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 5832, 1 and 5832 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 5832 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 as a factor, because 5832/1.5 = 3888, and it is not a whole number.
Mistake 4
Confusing Factors With Prime Numbers
Remember that factors can be any whole numbers, not just primes. For example, thinking all the factors of 5832 are prime numbers.
For example, 2 and 3 are the prime factors of 5832, but it has other factors like 4, 36.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 5832 as 23 × 36 and missing all the key factors.
Factors of 5832 Examples
Problem 1
A cake is cut into 5832 pieces. If you want to distribute them equally among 27 people, how many pieces will each person receive?
Each person will receive 216 pieces.
Explanation
To distribute the pieces equally, divide the total pieces by the number of people.
5832/27 = 216
Problem 2
A rectangular garden has a length of 54 meters and an area of 5832 square meters. What is the width of the garden?
108 meters.
Explanation
To find the width of the garden, use the formula,
Area = length × width
5832 = 54 × width
To find the value of width, shift 54 to the left side.
5832/54 = width
Width = 108.
Problem 3
A company has 5832 units of a product and wants to pack them into boxes, each containing 81 units. How many boxes will they need?
They will need 72 boxes.
Explanation
To find the number of boxes needed, divide the total units by the units per box.
5832/81 = 72
Problem 4
During a charity event, 5832 items are to be distributed among 108 families. How many items will each family receive?
Each family will receive 54 items.
Explanation
Dividing the items by the total number of families gives the number of items per family.
5832/108 = 54
Problem 5
A warehouse has 5832 crates of merchandise, and they need to be placed on 12 pallets evenly. How many crates will each pallet hold?
Each pallet will hold 486 crates.
Explanation
Divide the total crates by the number of pallets.
5832/12 = 486
FAQs on Factors of 5832
1.What are the factors of 5832?
2.Mention the prime factors of 5832.
3.Is 5832 a multiple of 9?
4.Mention the factor pairs of 5832?
5.What is the cube root of 5832?
Important Glossaries for Factors of 5832
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 5832 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 27, 36, 54, 81, 108, 162, 216, 324, 486, 648, 972, 1458, 1944, 2916, and 5832.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of 5832.
- 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 5832 are (1, 5832), (2, 2916), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 5832 is 23 × 36.
- Multiple: A number that can be divided by another number without a remainder. For example, 5832 is a multiple of 9.
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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.
Fun Fact
: She loves to read number jokes and games.
