103 LearnersLast updated on May 26th, 2025
Factors of -864
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 -864, how they are used in real life, and tips to learn them quickly.
What are the Factors of -864?
The numbers that divide -864 evenly are known as factors of -864.
A factor of -864 is a number that divides the number without remainder.
The positive factors of -864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, and 864.
Negative factors of -864: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -27, -32, -36, -48, -54, -72, -96, -108, -144, -216, -288, -432, and -864.
Prime factors of -864: 2 and 3.
Prime factorization of -864: -1 × 25 × 33.
The sum of positive factors of 864: 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 16 + 18 + 24 + 27 + 32 + 36 + 48 + 54 + 72 + 96 + 108 + 144 + 216 + 288 + 432 + 864 = 2,520.
How to Find Factors of -864?
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 -864. Identifying the numbers which are multiplied to get the number -864 is the multiplication method.
Step 1: Multiply -864 by 1, -864 × 1 = -864.
Step 2: Check for other numbers that give -864 after multiplying. For example:
2 × -432 = -864
3 × -288 = -864
4 × -216 = -864
6 × -144 = -864
8 × -108 = -864
9 × -96 = -864
12 × -72 = -864
16 × -54 = -864
18 × -48 = -864
24 × -36 = -864
Therefore, the positive factor pairs of -864 are: (1, -864), (2, -432), (3, -288), (4, -216), (6, -144), (8, -108), (9, -96), (12, -72), (16, -54), (18, -48), (24, -36).
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 -864 by 1, -864 ÷ 1 = -864.
Step 2: Continue dividing -864 by the numbers until the remainder becomes 0.
-864 ÷ 1 = -864
-864 ÷ 2 = -432
-864 ÷ 3 = -288
-864 ÷ 4 = -216
-864 ÷ 6 = -144
-864 ÷ 8 = -108
-864 ÷ 9 = -96
-864 ÷ 12 = -72
-864 ÷ 16 = -54
-864 ÷ 18 = -48
-864 ÷ 24 = -36
Therefore, the factors of -864 are: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864.
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 factor tree
Using Prime Factorization: In this process, prime factors of -864 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
-864 ÷ 2 = -432
-432 ÷ 2 = -216
-216 ÷ 2 = -108
-108 ÷ 2 = -54
-54 ÷ 2 = -27
-27 ÷ 3 = -9
-9 ÷ 3 = -3
-3 ÷ 3 = -1
The prime factors of -864 are 2 and 3. The prime factorization of -864 is: -1 × 25 × 33.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, -864 is divided by 2 to get -432.
Step 2: Now divide -432 by 2 to get -216.
Step 3: Then divide -216 by 2 to get -108.
Step 4: Divide -108 by 2 to get -54.
Step 5: Divide -54 by 2 to get -27.
Step 6: Divide -27 by 3 to get -9.
Step 7: Divide -9 by 3 to get -3.
Step 8: Divide -3 by 3 to get -1.
Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -864 is: -1 × 2^5 × 3^3.
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 -864: (1, -864), (2, -432), (3, -288), (4, -216), (6, -144), (8, -108), (9, -96), (12, -72), (16, -54), (18, -48), (24, -36).
Negative factor pairs of -864: (-1, 864), (-2, 432), (-3, 288), (-4, 216), (-6, 144), (-8, 108), (-9, 96), (-12, 72), (-16, 54), (-18, 48), (-24, 36).
Common Mistakes and How to Avoid Them in Factors of -864
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 -864, 1 and -864 are also factors.
Factors of -864 Examples
Problem 1
There are 18 students and -864 candies. How will they divide it equally?
They will get -48 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students. -864/18 = -48
Problem 2
A rectangle has a width of 12 meters and a total area of -864 square meters. Find the length.
-72 meters.
Explanation
To find the length of the rectangle, we use the formula, Area = length × width -864 = length × 12
To find the value of length, we need to shift 12 to the left side. -864/12 = length
Length = -72
Problem 3
There are 24 boxes and -864 marbles. How many marbles will be in each box?
Each box will have -36 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the boxes. -864/24 = -36
Problem 4
In a warehouse, there are -864 items and 27 containers. How many items are there in each container?
There are -32 items in each container.
Explanation
Dividing the items by the total containers, we will get the number of items in each container. -864/27 = -32
Problem 5
-864 books need to be distributed across 18 shelves. How many books will go on each shelf?
Each shelf will have -48 books.
Explanation
Divide the total books by shelves. -864/18 = -48
FAQs on Factors of -864
1.What are the factors of -864?
2.Mention the prime factors of -864.
3.Is -864 a multiple of 6?
4.Mention the factor pairs of -864.
5.What is the absolute value of -864?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of -864?
7.What are some fun ways kids in United Kingdom can practice Factors of -864 with numbers?
8.What role do numbers and Factors of -864 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of -864 skills?
Important Glossaries for Factors of -864
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -864 are 1, 2, 3, 4, 6, etc.
- Prime factors: The factors that are prime numbers. For example, 2 and 3 are the prime factors of -864.
- 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 -864 are (1, -864), (2, -432), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For example, -864 = -1 × 25 × 33.
- Absolute value: The non-negative value of a number without regard to its sign. For example, the absolute value of -864 is 864.
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About BrightChamps in United Kingdom
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.
