122 LearnersLast updated on May 26th, 2025
Factors of -108
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of -108, how they are used in real life, and tips to learn them quickly.
What are the Factors of -108?
The numbers that divide -108 evenly are known as factors of -108.
A factor of -108 is a number that divides the number without a remainder.
The factors of -108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
Negative factors of -108: -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, and -108.
Prime factors of -108: 2 and 3.
Prime factorization of -108: (-1) × 22 × 33.
The sum of factors of -108: 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280
How to Find Factors of -108?
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 -108. Identifying the numbers which are multiplied to get the number -108 is the multiplication method.
Step 1: Multiply -108 by -1, -108 × -1 = 108.
Step 2: Check for other numbers that give -108 after multiplying
2 × -54 = -108
3 × -36 = -108
4 × -27 = -108
6 × -18 = -108
9 × -12 = -108
Therefore, the positive factor pairs of -108 are: (1, -108), (2, -54), (3, -36), (4, -27), (6, -18), and (9, -12).
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 -108 by -1, -108 ÷ -1 = 108.
Step 2: Continue dividing -108 by the numbers until the remainder becomes 0.
-108 ÷ -1 = 108
-108 ÷ 2 = -54
-108 ÷ 3 = -36
-108 ÷ 4 = -27
-108 ÷ 6 = -18
-108 ÷ 9 = -12
Therefore, the factors of -108 are: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
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 -108 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-108 ÷ -1 = 108
108 ÷ 2 = 54
54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of -108 are 2 and 3.
The prime factorization of -108 is: (-1) × 22 × 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, -108 is divided by -1 to get 108.
Step 2: Now divide 108 by 2 to get 54.
Step 3: Then divide 54 by 2 to get 27.
Step 4: Divide 27 by 3 to get 9.
Step 5: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number that cannot be divided anymore. So, the prime factorization of -108 is: (-1) × 22 × 33.
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 -108: (1, -108), (2, -54), (3, -36), (4, -27), (6, -18), and (9, -12).
Negative factor pairs of -108: (-1, 108), (-2, 54), (-3, 36), (-4, 27), (-6, 18), and (-9, 12).
Common Mistakes and How to Avoid Them in Factors of -108
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 -108, 1 and -108 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 -108 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as factors. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -108/1.5 = -72, 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 -108 are prime numbers.
For example, 2 and 3 are the prime factors of -108, but it has other factors like 4, 12.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -108 as (-1) × 22 × 33 and missing all the key factors.
Factors of -108 Examples
Problem 1
There are 18 people and -108 apples. How will they distribute them equally?
They will get -6 apples each.
Explanation
To distribute the apples equally, we need to divide the total apples by the number of people.
-108/18 = -6
Problem 2
A rectangular billboard has a width of -4 meters and a total area of -108 square meters. Find the length?
27 meters.
Explanation
To find the length of the billboard, we use the formula,
Area = length × width
-108 = length × -4
To find the value of length, we need to shift -4 to the left side.
-108/-4 = length
Length = 27.
Problem 3
There are 12 crates and -108 oranges. How many oranges will be in each crate?
Each crate will have -9 oranges.
Explanation
To find the oranges in each crate, divide the total oranges by the crates.
-108/12 = -9
Problem 4
In a class, there are -108 students, and 6 groups. How many students are there in each group?
There are -18 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
-108/6 = -18
Problem 5
-108 books need to be placed in 9 boxes. How many books will go in each box?
Each of the boxes has -12 books.
Explanation
Divide total books by boxes.
-108/9 = -12
FAQs on Factors of -108
1.What are the factors of -108?
2.Mention the prime factors of -108.
3.Is -108 a multiple of 9?
4.Mention the factor pairs of -108?
5.What is the square of -108?
6.How can children in Singapore use numbers in everyday life to understand Factors of -108?
7.What are some fun ways kids in Singapore can practice Factors of -108 with numbers?
8.What role do numbers and Factors of -108 play in helping children in Singapore develop problem-solving skills?
9.How can families in Singapore create number-rich environments to improve Factors of -108 skills?
Important Glossaries for Factor of -108
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
- Prime factors: The factors which are prime numbers. For example, 2 and 3 are prime factors of -108.
- 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 -108 are (1, -108), (2, -54), etc.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, etc., are negative factors of -108.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of -108 is (-1) × 2^2 × 3^3.
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About BrightChamps in Singapore
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.
