101 LearnersLast updated on May 26th, 2025
Factors of -324
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 -324, how they are used in real life, and tips to learn them quickly.
What are the Factors of -324?
The numbers that divide -324 evenly are known as factors of -324.
A factor of -324 is a number that divides the number without a remainder.
The factors of -324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
Negative factors of -324: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -81, -108, -162, and -324.
Prime factors of -324: 2 and 3.
Prime factorization of -324: -2² × 3⁴.
The sum of factors of 324: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 81 + 108 + 162 + 324 = 945
How to Find Factors of -324?
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 -324. Identifying the numbers which are multiplied to get the number -324 is the multiplication method.
Step 1: Multiply -324 by 1, -324 × 1 = -324.
Step 2: Check for other numbers that give -324 after multiplying
2 × -162 = -324
3 × -108 = -324
4 × -81 = -324
6 × -54 = -324
9 × -36 = -324
12 × -27 = -324
18 × -18 = -324
Therefore, the positive factor pairs of -324 are: (1, -324), (2, -162), (3, -108), (4, -81), (6, -54), (9, -36), (12, -27), and (18, -18).
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 the simple division method
Step 1: Divide -324 by 1, -324 ÷ 1 = -324.
Step 2: Continue dividing -324 by the numbers until the remainder becomes 0.
-324 ÷ 1 = -324
-324 ÷ 2 = -162
-324 ÷ 3 = -108
-324 ÷ 4 = -81
-324 ÷ 6 = -54
-324 ÷ 9 = -36
-324 ÷ 12 = -27
-324 ÷ 18 = -18
Therefore, the factors of -324 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324.
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 -324 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-324 ÷ 2 = -162
-162 ÷ 2 = -81
-81 ÷ 3 = -27
-27 ÷ 3 = -9
-9 ÷ 3 = -3
-3 ÷ 3 = -1
The prime factors of -324 are 2 and 3.
The prime factorization of -324 is: -2² × 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, -324 is divided by 2 to get -162.
Step 2: Now divide -162 by 2 to get -81.
Step 3: Then divide -81 by 3 to get -27.
Step 4: Divide -27 by 3 to get -9.
Step 5: Divide -9 by 3 to get -3.
Step 6: Divide -3 by 3 to get -1. So, the prime factorization of -324 is: -2² × 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 -324: (1, -324), (2, -162), (3, -108), (4, -81), (6, -54), (9, -36), (12, -27), and (18, -18).
Negative factor pairs of -324: (-1, 324), (-2, 162), (-3, 108), (-4, 81), (-6, 54), (-9, 36), (-12, 27), and (-18, 18).
Common Mistakes and How to Avoid Them in Factors of -324
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 -324, 1 and -324 is also a factor.
Factors of -324 Examples
Problem 1
A dance troupe has 18 dancers and -324 dance steps to practice. How many steps will each dancer practice if the steps are divided evenly?
Each dancer will practice 18 steps.
Explanation
To divide the dance steps equally, we need to divide the total steps by the number of dancers.
-324/18 = -18
Problem 2
A baker is making cakes and has a large batch of -324 grams of flour. If each cake requires 27 grams, how many cakes can be made?
12 cakes.
Explanation
To find the number of cakes, divide the total flour by the flour required for each cake.
-324/27 = -12
Problem 3
A garden is organized into 3 sections, and there are -324 plants to distribute. How many plants will go into each section?
Each section will have 108 plants.
Explanation
To find the plants in each section, divide the total plants by the sections.
-324/3 = -108
Problem 4
A printing company has an order for -324 flyers and wants to divide them equally among 6 employees. How many flyers will each employee handle?
Each employee will handle 54 flyers.
Explanation
Dividing the flyers by the total employees, we will get the number of flyers each handles.
-324/6 = -54
Problem 5
A music teacher has -324 sheets of music to distribute among 9 students. How many sheets will each student get?
Each student will get 36 sheets.
Explanation
Divide total sheets by students.
-324/9 = -36
FAQs on Factors of -324
1.What are the factors of -324?
2.Mention the prime factors of -324.
3.Is -324, a multiple of 9?
4.Mention the factor pairs of -324?
5.What is the square of -324?
6.How can children in Qatar use numbers in everyday life to understand Factors of -324?
7.What are some fun ways kids in Qatar can practice Factors of -324 with numbers?
8.What role do numbers and Factors of -324 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of -324 skills?
Important Glossaries for Factor of -324
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, and 324.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of -324.
- 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 -324 are (1, -324), (2, -162), etc.
- Negative factors: Factors that are negative integers. For example, -1, -2, -3, etc., are negative factors of -324.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of -324 is -2² × 3⁴.
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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.
