100 LearnersLast updated on May 26th, 2025
Factors of 728
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 728, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 728?
The numbers that divide 728 evenly are known as factors of 728.
A factor of 728 is a number that divides the number without remainder.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728.
Negative factors of 728: -1, -2, -4, -7, -8, -13, -14, -26, -28, -52, -56, -91, -104, -182, -364, and -728.
Prime factors of 728: 2, 7, and 13.
Prime factorization of 728: 23 × 7 × 13.
The sum of factors of 728: 1 + 2 + 4 + 7 + 8 + 13 + 14 + 26 + 28 + 52 + 56 + 91 + 104 + 182 + 364 + 728 = 1678
How to Find Factors of 728?
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 728. Identifying the numbers which are multiplied to get the number 728 is the multiplication method.
Step 1: Multiply 728 by 1, 728 × 1 = 728.
Step 2: Check for other numbers that give 728 after multiplying
2 × 364 = 728
4 × 182 = 728
7 × 104 = 728
8 × 91 = 728
13 × 56 = 728
14 × 52 = 728
26 × 28 = 728
Therefore, the positive factor pairs of 728 are: (1, 728), (2, 364), (4, 182), (7, 104), (8, 91), (13, 56), (14, 52), (26, 28).
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 a simple division method:
Step 1: Divide 728 by 1, 728 ÷ 1 = 728.
Step 2: Continue dividing 728 by the numbers until the remainder becomes 0.
728 ÷ 1 = 728
728 ÷ 2 = 364
728 ÷ 4 = 182
728 ÷ 7 = 104
728 ÷ 8 = 91
728 ÷ 13 = 56
728 ÷ 14 = 52
728 ÷ 26 = 28
Therefore, the factors of 728 are: 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728.
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 728 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
728 ÷ 2 = 364
364 ÷ 2 = 182
182 ÷ 2 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1
The prime factors of 728 are 2, 7, and 13.
The prime factorization of 728 is: 23 × 7 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 728 is divided by 2 to get 364.
Step 2: Now divide 364 by 2 to get 182.
Step 3: Then divide 182 by 2 to get 91.
Step 4: Divide 91 by 7 to get 13. Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 728 is: 23 × 7 × 13.
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 728: (1, 728), (2, 364), (4, 182), (7, 104), (8, 91), (13, 56), (14, 52), (26, 28).
Negative factor pairs of 728: (-1, -728), (-2, -364), (-4, -182), (-7, -104), (-8, -91), (-13, -56), (-14, -52), (-26, -28).
Common Mistakes and How to Avoid Them in Factors of 728
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 word. Always remember to include 1 and the number itself.
For example, in factors of 728, 1 and 728 are also factors.
Factors of 728 Examples
Problem 1
There are 7 boxes and 728 apples. How will they distribute them equally?
They will get 104 apples each.
Explanation
To divide the apples equally, we need to divide the total apples by the number of boxes.
728/7 = 104
Problem 2
A rectangular garden has a length of 13 meters and a total area of 728 square meters. Find the width?
56 meters.
Explanation
To find the width of the garden, use the formula, Area = length × width 728 = 13 × width
To find the value of width, shift 13 to the left side.
728/13 = width
Width = 56.
Problem 3
There are 8 tables and 728 chairs. How many chairs will be at each table?
Each table will have 91 chairs.
Explanation
To find the chairs at each table, divide the total chairs by the tables.
728/8 = 91
Problem 4
In a theater, there are 728 seats, and 14 rows. How many seats are there in each row?
There are 52 seats in each row.
Explanation
Dividing the seats by the total rows, we will get the number of seats in each row.
728/14 = 52
Problem 5
728 pages need to be arranged in 26 binders. How many pages will go in each binder?
Each binder will have 28 pages.
Explanation
Divide total pages by binders.
728/26 = 28
FAQs on Factors of 728
1.What are the factors of 728?
2.Mention the prime factors of 728.
3.Is 728 a multiple of 8?
4.Mention the factor pairs of 728?
5.What is the square of 728?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 728?
7.What are some fun ways kids in United Kingdom can practice Factors of 728 with numbers?
8.What role do numbers and Factors of 728 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 728 skills?
Important Glossaries for Factor of 728
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, and 728.
- Prime factors: The factors which are prime numbers. For example, 2, 7, and 13 are prime factors of 728.
- 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 728 are (1, 728), (2, 364), etc.
- Prime factorization: Expressing a number as the product of its prime factors. For 728, it is 2^3 × 7 × 13.
- Multiple: A number is a multiple of another if it can be divided by that number without a remainder. For example, 728 is a multiple of 8.
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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
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