116 LearnersLast updated on May 26th, 2025
Factors of 27000
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 27000, how they are used in real life, and tips to learn them quickly.
What are the Factors of 27000?
The numbers that divide 27000 evenly are known as factors of 27000.
A factor of 27000 is a number that divides the number without remainder.
The factors of 27000 include 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 75, 90, 108, 135, 150, 180, 225, 270, 300, 450, 540, 675, 900, 1350, 1800, 2700, 4500, 5400, 9000, 13500, and 27000.
Negative factors of 27000: -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -75, -90, -108, -135, -150, -180, -225, -270, -300, -450, -540, -675, -900, -1350, -1800, -2700, -4500, -5400, -9000, -13500, and -27000.
Prime factors of 27000: 2, 3, and 5.
Prime factorization of 27000: 23 × 33 × 53.
The sum of factors of 27000: 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 27 + 30 + 36 + 45 + 54 + 60 + 75 + 90 + 108 + 135 + 150 + 180 + 225 + 270 + 300 + 450 + 540 + 675 + 900 + 1350 + 1800 + 2700 + 4500 + 5400 + 9000 + 13500 + 27000 = 97278
How to Find Factors of 27000?
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 27000. Identifying the numbers which are multiplied to get the number 27000 is the multiplication method.
Step 1: Multiply 27000 by 1, 27000 × 1 = 27000.
Step 2: Check for other numbers that give 27000 after multiplying
2 × 13500 = 27000
3 × 9000 = 27000
5 × 5400 = 27000
6 × 4500 = 27000
Therefore, some positive factor pairs of 27000 are: (1, 27000), (2, 13500), (3, 9000), (5, 5400), (6, 4500). 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 as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 27000 by 1, 27000 ÷ 1 = 27000.
Step 2: Continue dividing 27000 by the numbers until the remainder becomes 0.
27000 ÷ 1 = 27000
27000 ÷ 2 = 13500
27000 ÷ 3 = 9000
27000 ÷ 5 = 5400
27000 ÷ 6 = 4500
Therefore, some factors of 27000 are: 1, 2, 3, 5, 6, 9, and so on.
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 27000 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
27000 ÷ 2 = 13500
13500 ÷ 2 = 6750
6750 ÷ 2 = 3375
3375 ÷ 3 = 1125
1125 ÷ 3 = 375
375 ÷ 3 = 125
125 ÷ 5 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 27000 are 2, 3, and 5.
The prime factorization of 27000 is: 23 × 33 × 53.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 27000 is divided by 2 to get 13500.
Step 2: Now divide 13500 by 2 to get 6750.
Step 3: Then divide 6750 by 2 to get 3375.
Step 4: Divide 3375 by 3 to get 1125. This process continues until we reach the prime number 5. So, the prime factorization of 27000 is: 23 × 33 × 53.
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 27000: (1, 27000), (2, 13500), (3, 9000), (5, 5400), (6, 4500), etc.
Negative factor pairs of 27000: (-1, -27000), (-2, -13500), (-3, -9000), (-5, -5400), (-6, -4500), etc.
Common Mistakes and How to Avoid Them in Factors of 27000
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 27000, 1 and 27000 are also factors.
Mistake 2
Missing Negative Factors
We often mention only positive factors. There are also negative factors, so always check whether you have mentioned negative factors
For example, the factors of 27000 include -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 1.5 is a factor because 27000/1.5 = 18000, 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 27000 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 27000, but it has other factors like 4, 10, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 27000 as 2^3 × 3^3 × 5^3 and missing all the key factors.
Factors of 27000 Examples
Problem 1
There are 12 teams and 27000 points. How will they divide the points equally?
Each team will get 2250 points.
Explanation
To divide the points equally, we need to divide the total points by the number of teams.
27000/12 = 2250
Problem 2
A swimming pool is rectangular, the length of the pool is 60 meters and the total area is 27000 square meters. Find the width.
450 meters.
Explanation
To find the width of the pool, we use the formula,
Area = length × width
27000 = 60 × width
To find the value of width, we need to shift 60 to the left side.
27000/60 = width
Width = 450.
Problem 3
There are 18 trucks and 27000 kilograms of cargo. How much will each truck carry?
Each truck will carry 1500 kilograms.
Explanation
To find the cargo for each truck, divide the total cargo by the number of trucks.
27000/18 = 1500
Problem 4
In a stadium, there are 9 sections, and 27000 seats. How many seats are there in each section?
There are 3000 seats in each section.
Explanation
Dividing the seats by the total sections, we get the number of seats in each section.
27000/9 = 3000
Problem 5
27000 books need to be arranged in 90 bookshelves. How many books will go on each shelf?
Each of the shelves will have 300 books.
Explanation
Divide total books by shelves.
27000/90 = 300
FAQs on Factors of 27000
1.What are the factors of 27000?
2.Mention the prime factors of 27000.
3.Is 27000 a multiple of 9?
4.Mention the factor pairs of 27000?
5.What is the cube of 30?
6.How can children in Qatar use numbers in everyday life to understand Factors of 27000?
7.What are some fun ways kids in Qatar can practice Factors of 27000 with numbers?
8.What role do numbers and Factors of 27000 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve Factors of 27000 skills?
Important Glossaries for Factors of 27000
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 27000 include 1, 2, 3, 5, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 27000.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, some factor pairs of 27000 are (1, 27000), (2, 13500), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 27000 is 23 × 33 × 53.
- Negative factors: Factors that are negative numbers. For example, -1, -2, -3, etc., are negative factors of 27000.
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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.
