126 LearnersLast updated on May 26th, 2025
Factors of -135
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 -135, how they are used in real life, and tips to learn them quickly.
What are the Factors of -135?
The numbers that divide -135 evenly are known as factors of -135. A factor of -135 is a number that divides the number without a remainder.
The factors of -135 are 1, 3, 5, 9, 15, 27, 45, and 135.
Negative factors of -135: -1, -3, -5, -9, -15, -27, -45, and -135.
Prime factors of -135: 3 and 5.
Prime factorization of -135: 33 × 51
The sum of positive factors of 135 (ignoring the negative sign): 1 + 3 + 5 + 9 + 15 + 27 + 45 + 135 = 240
How to Find Factors of -135?
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 are multiplied to give -135. Identifying the numbers which are multiplied to get the number -135 is the multiplication method.
Step 1: Multiply -135 by 1, -135 × 1 = -135.
Step 2: Check for other numbers that give -135 after multiplying: 3 × -45 = -135 5 × -27 = -135 9 × -15 = -135 (Additionally consider negative factor pairs similarly)
Therefore, the positive factor pairs of -135 are: (1, 135), (3, 45), (5, 27), (9, 15). For every positive factor, there is a corresponding 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 the simple division method:
Step 1: Divide -135 by 1, -135 ÷ 1 = -135.
Step 2: Continue dividing -135 by the numbers until the remainder becomes 0. -135 ÷ 1 = -135 -135 ÷ 3 = -45 -135 ÷ 5 = -27 -135 ÷ 9 = -15
Therefore, the factors of -135 are: 1, 3, 5, 9, 15, 27, 45, 135.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 -135 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1. -135 ÷ 3 = -45 -45 ÷ 3 = -15 -15 ÷ 3 = -5 -5 ÷ 5 = -1 The prime factors of -135 are 3 and 5.
The prime factorization of -135 is: 33 × 51
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, -135 is divided by 3 to get -45.
Step 2: Now divide -45 by 3 to get -15.
Step 3: Then divide -15 by 3 to get -5.
Step 4: Divide -5 by 5 to get -1.
Here, -1 is the smallest factor, and 3 and 5 are prime numbers, that cannot be divided anymore.
So, the prime factorization of -135 is: 33 × 51.
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 -135: (1, 135), (3, 45), (5, 27), (9, 15).
Negative factor pairs of -135: (-1, -135), (-3, -45), (-5, -27), (-9, -15).
Common Mistakes and How to Avoid Them in Factors of -135
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 -135, 1 and -135 are also factors.
Mistake 2
Missing Negative Factors
We often use only positive factors. There are also negative factors; always check whether you have mentioned negative factors. For example, the factors of -135 include -1, -3, -5, etc.
Mistake 3
Including the Fraction
Children might sometimes incorrectly include fractions as factors. Only whole numbers can be factors.
For example, thinking 1.5 is a factor because -135/1.5 = -90, 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 -135 are prime numbers. For example, 3 and 5 are the prime factors of -135, but it has other factors like 9, 15.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking -135 as \(3^3 \times 5 \times -1\) and missing all the key factors.
Factors of -135 Examples
Problem 1
There are 15 students and -135 points to distribute. How will the points be distributed equally?
Each student receives -9 points.
Explanation
To distribute the points equally, we need to divide the total points by the number of students. -135 ÷ 15 = -9
Problem 2
A playground is rectangular, the width of the playground is 9 meters and the total area is -135 square meters. Find the length.
-15 meters.
Explanation
To find the length of the playground, we use the formula, Area = length × width
-135 = length × 9
To find the value of length, we need to divide by 9.
-135 ÷ 9 = length
Length = -15.
Problem 3
There are 27 boxes and -135 items. How many items will be in each box?
Each box will have -5 items.
Explanation
To find the items in each box, divide the total items by the number of boxes. -135 ÷ 27 = -5
Problem 4
In a class, there are -135 students, and 5 groups. How many students are there in each group?
There are -27 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group. -135 ÷ 5 = -27
Problem 5
135 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 45 books.
Explanation
Divide total books by shelves. 135 ÷ 3 = 45
FAQs on Factors of -135
1.What are the factors of -135?
2.Mention the prime factors of -135.
3.Is -135 a multiple of 9?
4.Mention the factor pairs of -135?
5.What is the square of -135?
6.How can children in Qatar use numbers in everyday life to understand Factors of -135?
7.What are some fun ways kids in Qatar can practice Factors of -135 with numbers?
8.What role do numbers and Factors of -135 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of -135 skills?
Important Glossaries for Factors of -135
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -135 are 1, 3, 5, 9, 15, 27, 45, 135, and their negatives.
- Prime factors: The factors which are prime numbers. For example, 3 and 5 are prime factors of -135.
- 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 -135 are (1, -135), (3, -45), etc.
- Negative factors: Negative numbers that divide the given number without leaving a remainder. For example, -1, -3, -5 are negative factors of -135.
- Prime factorization: Expressing a number as a product of its prime factors. For example, the prime factorization of -135 is \(3^3 \times 5 \times -1\).
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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.
