102 LearnersLast updated on May 26th, 2025
Factors of -270
Factors are the numbers that divide any given number evenly without 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 -270, how they are used in real life, and the tips to learn them quickly.
What are the Factors of -270?
The numbers that divide -270 evenly are known as factors of -270.
A factor of -270 is a number that divides the number without remainder.
The positive factors of -270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.
Including their negative counterparts, the factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -90, -135, and -270.
Prime factors of 270: 2, 3, and 5.
Prime factorization of 270: 2 × 33 × 5.
The sum of the positive factors of 270: 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 + 270 = 810.
How to Find Factors of -270?
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 -270. Identifying the numbers which are multiplied to get the number -270 is the multiplication method.
Step 1: Multiply -270 by 1, -270 × 1 = -270.
Step 2: Check for other numbers that give -270 after multiplying
-1 × 270 = -270
-2 × 135 = -270
-3 × 90 = -270
-5 × 54 = -270
-6 × 45 = -270
-9 × 30 = -270
-10 × 27 = -270
-15 × 18 = -270
Therefore, the negative factor pairs of -270 are: (-1, 270), (-2, 135), (-3, 90), (-5, 54), (-6, 45), (-9, 30), (-10, 27), (-15, 18).
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 in whole numbers as factors. Factors can be calculated by following the simple division method
Step 1: Divide -270 by 1, -270 ÷ 1 = -270.
Step 2: Continue dividing -270 by the numbers until the remainder becomes 0.
-270 ÷ 1 = -270
-270 ÷ 2 = -135
-270 ÷ 3 = -90
-270 ÷ 5 = -54
-270 ÷ 6 = -45
-270 ÷ 9 = -30
-270 ÷ 10 = -27
-270 ÷ 15 = -18
Therefore, the positive factors of 270 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Prime Factors and Prime Factorization
The factors can be found by dividing 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 270 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
270 ÷ 2 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
The prime factors of 270 are 2, 3, and 5.
The prime factorization of 270 is: 2 × 33 × 5.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 270 is divided by 2 to get 135.
Step 2: Now divide 135 by 3 to get 45.
Step 3: Then divide 45 by 3 to get 15.
Step 4: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, which cannot be divided anymore. So, the prime factorization of 270 is: 2 × 33 × 5.
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 270: (1, 270), (2, 135), (3, 90), (5, 54), (6, 45), (9, 30), (10, 27), (15, 18).
Negative factor pairs of -270: (-1, 270), (-2, 135), (-3, 90), (-5, 54), (-6, 45), (-9, 30), (-10, 27), (-15, 18).
Common Mistakes and How to Avoid Them in Factors of -270
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 factors for every number. Always remember to include 1 and the number itself.
For example, in factors of -270, 1 and -270 are also factors.
Factors of -270 Examples
Problem 1
There are 9 teams and each team needs -270 points to qualify for the next round. How many points does each team need to secure?
Each team needs -30 points.
Explanation
To find the points each team needs, divide the total points by the number of teams.
-270/9 = -30
Problem 2
A rectangular parking lot has a length of 18 meters and a total area of -270 square meters. What is the width?
-15 meters.
Explanation
To find the width of the parking lot, we use the formula,
Area = length × width
-270 = 18 × width
To find the value of width, shift 18 to the left side.
-270/18 = width
Width = -15.
Problem 3
There are 54 containers and -270 liters of oil. How many liters will be in each container?
Each container will have -5 liters.
Explanation
To find the liters in each container, divide the total liters by the number of containers.
-270/54 = -5
Problem 4
In a chess tournament, there are -270 matches and 10 rounds. How many matches are there in each round?
There are -27 matches in each round.
Explanation
Dividing the matches by the total rounds, we get the number of matches in each round.
-270/10 = -27
Problem 5
-270 books need to be arranged in 15 shelves. How many books will go on each shelf?
Each of the shelves has -18 books.
Explanation
Divide the total books by the number of shelves.
-270/15 = -18
FAQs on Factors of -270
1.What are the factors of -270?
2.Mention the prime factors of -270.
3.Is -270 a multiple of 3?
4.Mention the factor pairs of -270?
5.What is the square of -270?
6.How can children in Australia use numbers in everyday life to understand Factors of -270?
7.What are some fun ways kids in Australia can practice Factors of -270 with numbers?
8.What role do numbers and Factors of -270 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of -270 skills?
Important Glossaries for Factors of -270
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of -270 include 1, 2, 3, 5, etc.
- Negative factors: The negative counterparts of the positive factors of a number. For example, -1, -2, -3, -5, etc., are the negative factors of -270.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 270.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, (-1, 270) and (-2, 135) are factor pairs of -270.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 270 is 2 × 33 × 5.
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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.
