183 LearnersLast updated on May 26th, 2025
Factors Of 81
A number which divides another number exactly without leaving a remainder is called a factor of the given number. Factors play an important role in many real-life situations. They are useful in deciding the best time to schedule work shifts and events.
What are the Factors of 81?
Factors often come in pairs. There are several methods to figure them out, which you'll be learning about in a second. For now let's just focus on the factors of 81, which are mentioned below:
Negative factors of 81: -1, -3, -9, -27, -81
Prime factors of 81: 3
Prime factorization of 81: 34
The sum of factors of 81: 1 + 3 + 9 + 27 + 81= 121
How To Find The Factors of 81?
For finding factors, school kids use different methods for easy calculation. A few commonly used methods are as follows:
- Use of Multiplication Method
- Use of Division Method
- Use of Prime Factors and Prime Factorization.
So, here we discuss a detailed explanation of the following methods:
Finding Factors Using Multiplication Method
In the multiplication method, we will try to find out the numbers that multiply together to give the value, 81. We will check the factors step by step:
Step 1: Start to multiply with numbers, which gives the value of 81.
Start with 1, and continue to multiply with other numbers.
1 × 81 = 81
3 × 27 = 81
9 × 9 = 81
Step 2: After the calculation, we get to these numbers, the factors of 81.
Step 3: The positive factor pairs of 81 found through multiplication are (1,81), (3,27), and (9,9)
Step 4: The negative factor pairs of 81 are (-1, -81), (-3, -27), and (-9, -9)
Finding Factors Using Division Method
Using this method we will break down the given number till our remainder is zero. Let us go through the step-by-step process to find the factors of 81:
Step 1: Divide 81 by smaller numbers and see if there is any remainder. E.g., 81/1 = 81.
Step 2: We will continue in the same way and check for other numbers as well. For 81, the factors are 1, 3, 9, 27, and 81 because 81 can be divided evenly by these numbers.
Prime Factors and Prime Factorization
The prime factor of 81 is 3. The prime factors can be found using the methods given below:
- Prime Factorization
- Factor Tree
By Using Prime Factorization: It is a method in which we break down a number into its prime factor.
3 is the smallest prime number, so start dividing with two. And then continue to divide with other prime numbers.
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factorization of 81 is :
81 = 34
With prime factorization, 81 can be broken down into prime factors 3.
Using Factor Tree
A factor tree is a visual representation of breaking a number into its prime factors. It is an easy and simple way to present the factors.
Step 1: 81 divided by 3 gives us the quotient 27.
Step 2: Since 27 is not a prime number, it can be divided further.
The prime factorization of 81 is written below :
81 = 34
Factor Pairs
Every number has either a positive or negative factor. Let us look at those sets of factors.
Positive pair Factors:(1,81), (3,27), and (9,9)
Negative pair Factors: (-1,-81), (-3,-27), and (-9,-9)
Common Mistakes and How to Avoid Them While Solving Factors Of 81
Children tend to make mistakes while finding the factors of a number. Let us look at how to avoid those mistakes.
Mistake 1
Confusing Factors with Multiples
The factors of a number can divide the given number without any remainder, whereas multiples are the products of multiplying the number by an integer. For example for 12, the factors are 1, 2, 3, 4, 6, and 12. And the multiples are 12, 24, and 36, etc… To avoid this confusion, always understand the concept separately.
Factors Of 81 Examples
Problem 1
A garden fence is 81 meters long. Can it be divided into 3-meter sections?
Yes, 27 sections.
Explanation
Yes, the garden fence can be divided into 3-meter sections. 81÷ 3 equals 27, with no leftovers. So, 3 is a factor of 81. There are 27 sections.
Problem 2
If a ribbon is 81 cm long, can it be cut into equal pieces of 27 cm?
Yes, 3 pieces.
Explanation
We will get 3 equal pieces. First, we divide 81 by 27, and we get 3 without any remainder. This means the number 27 is a factor of 81. Factors divide evenly without any remainder.
Problem 3
A classroom has 81 chairs, and they need to be arranged in rows of 9 chairs. How many rows can be formed?
A total of 9 rows of chairs can be formed.
Explanation
An easy way to find the number of rows is to divide the total number of chairs by the number of chairs in each row.
81 ÷ 9 = 9
FAQs on Factors Of 81
1.What is the LCM of 81 and 27?
2.Is 81 a factor of 16?
3.Is 81 a prime factor?
4.What are the multiples of 81?
5.What is the GCF of 81 and 54?
6.How can children in Thailand use numbers in everyday life to understand Factors Of 81?
7.What are some fun ways kids in Thailand can practice Factors Of 81 with numbers?
8.What role do numbers and Factors Of 81 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve Factors Of 81 skills?
Important Glossaries For Factors Of 81
- Factors: Factors are numbers that divide a given number exactly, without any remainder. For example, 6 is divisible by 1, 2, 3, and 6. Therefore, 1, 2, 3, and 6 are the factors of 6.
- Prime Factors: Prime factors of a number are a set of prime numbers that multiply together to give the original number. For 81, the prime factor is 3.
- Multiples: We get multiples when we multiply a number by another number. Let’s take some multiples of 2 (2, 4, 6, and so on).
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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.
