125 LearnersLast updated on May 26th, 2025
Factors of 729
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 729, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 729?
The numbers that divide 729 evenly are known as factors of 729.
A factor of 729 is a number that divides the number without remainder.
The factors of 729 are 1, 3, 9, 27, 81, 243, and 729.
Negative factors of 729: -1, -3, -9, -27, -81, -243, and -729.
Prime factors of 729: 3.
Prime factorization of 729: 36
The sum of factors of 729: 1 + 3 + 9 + 27 + 81 + 243 + 729 = 1093
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How to Find Factors of 729?
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 729. Identifying the numbers which are multiplied to get the number 729 is the multiplication method.
Step 1: Multiply 729 by 1, 729 × 1 = 729.
Step 2: Check for other numbers that give 729 after multiplying
3 × 243 = 729
9 × 81 = 729
27 × 27 = 729
Therefore, the positive factor pairs of 729 are: (1, 729), (3, 243), (9, 81), (27, 27).
All these factor pairs result in 729.
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 729 by 1, 729 ÷ 1 = 729.
Step 2: Continue dividing 729 by the numbers until the remainder becomes 0.
729 ÷ 1 = 729
729 ÷ 3 = 243
729 ÷ 9 = 81
729 ÷ 27 = 27
Therefore, the factors of 729 are: 1, 3, 9, 27, 81, 243, and 729.
Prime Factors and Prime Factorization
The factors can be found by dividing them 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 729 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
729 ÷ 3 = 243
243 ÷ 3 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
The prime factor of 729 is 3. The prime factorization of 729 is: 36.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows
Step 1: Firstly, 729 is divided by 3 to get 243.
Step 2: Now divide 243 by 3 to get 81.
Step 3: Then divide 81 by 3 to get 27.
Step 4: Divide 27 by 3 to get 9.
Step 5: Divide 9 by 3 to get 3. Here, 3 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 729 is: 36.
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 729: (1, 729), (3, 243), (9, 81), and (27, 27).
Negative factor pairs of 729: (-1, -729), (-3, -243), (-9, -81), and (-27, -27).
Common Mistakes and How to Avoid Them in Factors of 729
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 the factors for every word. Always remember to include 1 and the number itself.
For example, in factors of 729, 1 and 729 are also factors.
Mistake 2
Missing Negative Factors
We have used only to mention positive factors every time. There are also negative factors, always check whether you have mentioned negative factors.
For example, the factors of 729 consist of -1, -3, -9, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a fraction. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 729/1.5 = 486, 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 729 are prime numbers.
For example, 3 is the prime factor of 729, but it has other factors like 9, 27.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up in writing wrong factors.
For example, not breaking 729 as 36 and missing all the key factors.
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Factors of 729 Examples
Problem 1
There are 9 people and 729 candies. How will they divide it equally?
They will get 81 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of people.
729/9 = 81
Problem 2
A square garden has an area of 729 square meters. What is the length of one side of the garden?
27 meters.
Explanation
To find the length of one side of the square garden, we use the formula for the area of a square, Area = side × side 729 = side × side
To find the value of the side, we take the square root of 729.
√729 = 27
Problem 3
There are 27 boxes and 729 marbles. How many marbles will be in each box?
Each box will have 27 marbles.
Explanation
To find the marbles in each box, divide the total marbles by the number of boxes.
729/27 = 27
Problem 4
In a tournament, there are 729 participants, and 81 teams. How many participants are there in each team?
There are 9 participants in each team.
Explanation
Dividing the participants by the total number of teams, we will get the number of participants in each team.
729/81 = 9
Problem 5
729 books need to be arranged in 3 shelves. How many books will go on each shelf?
Each of the shelves has 243 books.
Explanation
Divide the total books by the number of shelves.
729/3 = 243
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FAQs on Factors of 729
1.What are the factors of 729?
2.Mention the prime factors of 729.
3.Is 729 a multiple of 9?
4.Mention the factor pairs of 729?
5.What is the square root of 729?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 729?
7.What are some fun ways kids in United Kingdom can practice Factors of 729 with numbers?
8.What role do numbers and Factors of 729 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve Factors of 729 skills?
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Important Glossaries for Factors of 729
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 729 are 1, 3, 9, 27, 81, 243, and 729.
- Prime factors: The factors which are prime numbers. For example, 3 is a prime factor of 729.
- 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 729 are (1, 729), (3, 243), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 729 is 36.
- Negative factors: Factors that are negative, similar to positive factors but with a minus sign. For example, negative factors of 729 are -1, -3, -9, etc.
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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.
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