Last updated on May 26th, 2025
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.
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
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
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.
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).
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 18 people and -108 apples. How will they distribute them equally?
They will get -6 apples each.
To distribute the apples equally, we need to divide the total apples by the number of people.
-108/18 = -6
A rectangular billboard has a width of -4 meters and a total area of -108 square meters. Find the length?
27 meters.
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.
There are 12 crates and -108 oranges. How many oranges will be in each crate?
Each crate will have -9 oranges.
To find the oranges in each crate, divide the total oranges by the crates.
-108/12 = -9
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.
Dividing the students by the total groups, we will get the number of students in each group.
-108/6 = -18
-108 books need to be placed in 9 boxes. How many books will go in each box?
Each of the boxes has -12 books.
Divide total books by boxes.
-108/9 = -12
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.
: She loves to read number jokes and games.