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 -27, how they are used in real life, and the tips to learn them quickly.
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.
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 -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.
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.
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 -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.
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).
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 3 shelves and -27 books to arrange. How will they divide it equally?
Each shelf will have -9 books.
To divide the books equally, we need to divide the total books by the number of shelves.
-27/3 = -9
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.
To find out how many boxes are needed, divide the total number of cupcakes by the number each box can hold.
-27/9 = -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.
To find the number of bags, divide the total apples by the number of apples per bag.
-27/3 = -9
A company is distributing -27 pens equally among 9 departments. How many pens will each department receive?
Each department will receive -3 pens.
To find the number of pens each department will receive, divide the total pens by the number of departments. -27/9 = -3
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.
Divide the total number of plants by the number of plants per row.
-27/3 = -9
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.