103 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 factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270.
Negative factors of 270: -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 × 3^3 × 5.
The sum of factors of 270:
1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 + 270
= 768
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
2 × 135 = 270
3 × 90 = 270
5 × 54 = 270
6 × 45 = 270
9 × 30 = 270
10 × 27 = 270
15 × 18 = 270
Therefore, the positive factor pairs of 270 are: (1, 270), (2, 135), (3, 90), (5, 54), (6, 45), (9, 30), (10, 27), (15, 18).
All these factor pairs result in 270.
For every positive factor, there is a 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 in whole numbers as factors. Factors can be calculated by following a 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 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 it 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 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 × 3^3 × 5.
Factor Tree
The factor tree is a graphical representation of breaking down any number into prime factors. The following steps show
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, that cannot be divided anymore. So, the prime factorization of 270 is: 2 × 3^3 × 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), and (15, 18).
Negative factor pairs of 270: (-1, -270), (-2, -135), (-3, -90), (-5, -54), (-6, -45), (-9, -30), (-10, -27), and (-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 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 270, 1 and 270 are also factors.
Factors of 270 Examples
Problem 1
There are 27 participants and 270 ribbons. How will they divide it equally?
They will get 10 ribbons each.
Explanation
To divide the ribbons equally, we need to divide the total ribbons with the number of participants. 270/27 = 10
Problem 2
A garden is rectangular, the length of the garden is 18 meters and the total area is 270 square meters. Find the width?
15 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
270 = 18 × width
To find the value of width, we need to shift 18 to the left side.
270/18 = width
Width = 15.
Problem 3
There are 30 bags and 270 candies. How many candies will be in each bag?
Each bag will have 9 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
270/30 = 9
Problem 4
In a class, there are 270 students, and 9 groups. How many students are there in each group?
There are 30 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
270/9 = 30
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 total books with 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 9?
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 Factor of 270
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 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, the factor pairs of 270 are (1, 270), (2, 135), etc.
- Prime Factorization: Breaking down a number into its prime factors. For example, the prime factorization of 270 is 2 × 3^3 × 5.
- Multiples: A number that can be divided by another number without leaving a remainder. For example, 270 is a multiple of 9.
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About BrightChamps in Australia
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.
