124 LearnersLast updated on May 26th, 2025
Factors of -27
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 -27, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -27?
The numbers that divide -27 evenly are known as factors of -27.
A factor of -27 is a number that divides the number without remainder.
The factors of -27 are 1, 3, 9, and 27.
Negative factors of -27: -1, -3, -9, and -27.
Prime factors of -27: 3.
Prime factorization of -27: -1 × 3³.
The sum of factors of -27: 1 + 3 + 9 + 27 = 40.
How to Find Factors of -27?
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 -27. Identifying the numbers which are multiplied to get the number -27 is the multiplication method.
Step 1: Multiply -27 by -1, -27 × -1 = 27.
Step 2: Check for other numbers that give -27 after multiplying
-1 × 27 = -27
-3 × 9 = -27
Therefore, the positive factor pairs of -27 are: (1, 27), (3, 9).
For every positive factor, there is a corresponding 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 -27 by -1, -27 ÷ -1 = 27.
Step 2: Continue dividing -27 by the numbers until the remainder becomes 0.
-27 ÷ -1 = 27
-27 ÷ -3 = 9
Therefore, the factors of -27 are: 1, 3, 9, 27.
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 -27 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
-27 ÷ -3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factors of -27 are 3.
The prime factorization of -27 is: -1 × 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, -27 is divided by -3 to get 9.
Step 2: Now divide 9 by 3 to get 3.
Step 3: Then divide 3 by 3 to get 1. Here, 3 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of -27 is: -1 × 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 -27: (1, 27), (3, 9).
Negative factor pairs of -27: (-1, -27), (-3, -9).
Common Mistakes and How to Avoid Them in Factors of -27
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 -27, 1 and -27 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 -27 consist of -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because -27/1.5 = -18, and -18 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 -27 are prime numbers. For example, 3 is the prime factor of -27, but it has other factors like 9 and 27.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing incorrect factors.
For example, not breaking -27 as -1 × 3³ and missing key factors.
Factors of -27 Examples
Problem 1
There are 3 shelves and -27 books to arrange. How will they divide it equally?
Each shelf will have -9 books.
Explanation
To divide the books equally, we need to divide the total books by the number of shelves.
-27/3 = -9
Problem 2
A baker has -27 cupcakes to place in boxes, and each box can hold 9 cupcakes. How many boxes does the baker need?
The baker needs -3 boxes.
Explanation
To find out how many boxes are needed, divide the total number of cupcakes by the number each box can hold.
-27/9 = -3
Problem 3
A group of people want to split -27 apples into bags with 3 apples each. How many bags do they need?
They need -9 bags.
Explanation
To find the number of bags, divide the total apples by the number of apples per bag.
-27/3 = -9
Problem 4
A company is distributing -27 pens equally among 9 departments. How many pens will each department receive?
Each department will receive -3 pens.
Explanation
To find the number of pens each department will receive, divide the total pens by the number of departments. -27/9 = -3
Problem 5
A gardener has -27 plants and wants to create rows of 3 plants each. How many rows can he create?
He can create -9 rows.
Explanation
Divide the total number of plants by the number of plants per row.
-27/3 = -9
FAQs on Factors of -27
1.What are the factors of -27?
2.Mention the prime factors of -27.
3.Is -27 a multiple of 3?
4.Mention the factor pairs of -27?
5.What is the cube of 3?
6.How can children in Saudi Arabia use numbers in everyday life to understand Factors of -27?
7.What are some fun ways kids in Saudi Arabia can practice Factors of -27 with numbers?
8.What role do numbers and Factors of -27 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve Factors of -27 skills?
Important Glossaries for Factor of -27
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -27 are 1, 3, 9, and 27.
- Prime factors: The factors which are prime numbers. For example, 3 is a prime factor of -27.
- 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 -27 are (1, 27), (3, 9).
- Negative factors: Factors that are negative numbers. For example, -1, -3, -9, and -27 are the negative factors of -27.
- Prime factorization: The process of breaking down a number into its prime factors. For example, the prime factorization of -27 is -1 × 3³.
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About BrightChamps in Saudi Arabia
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.
