100 LearnersLast updated on May 26th, 2025
Factors of 726
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 726, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 726?
The numbers that divide 726 evenly are known as factors of 726.
A factor of 726 is a number that divides the number without remainder.
The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726.
Negative factors of 726: -1, -2, -3, -6, -11, -22, -33, -66, -121, -242, -363, and -726.
Prime factors of 726: 2, 3, and 11.
Prime factorization of 726: 2 × 3 × 112.
The sum of factors of 726: 1 + 2 + 3 + 6 + 11 + 22 + 33 + 66 + 121 + 242 + 363 + 726 = 1596
How to Find Factors of 726?
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 726. Identifying the numbers which are multiplied to get the number 726 is the multiplication method.
Step 1: Multiply 726 by 1, 726 × 1 = 726.
Step 2: Check for other numbers that give 726 after multiplying:
2 × 363 = 726
3 × 242 = 726
6 × 121 = 726
11 × 66 = 726
22 × 33 = 726
Therefore, the positive factor pairs of 726 are: (1, 726), (2, 363), (3, 242), (6, 121), (11, 66), (22, 33).
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 726 by 1, 726 ÷ 1 = 726.
Step 2: Continue dividing 726 by the numbers until the remainder becomes 0.
726 ÷ 1 = 726
726 ÷ 2 = 363
726 ÷ 3 = 242
726 ÷ 6 = 121
726 ÷ 11 = 66
726 ÷ 22 = 33
Therefore, the factors of 726 are: 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726.
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 726 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
726 ÷ 2 = 363
363 ÷ 3 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
The prime factors of 726 are 2, 3, and 11.
The prime factorization of 726 is: 2 × 3 × 112.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 726 is divided by 2 to get 363.
Step 2: Now divide 363 by 3 to get 121.
Step 3: Then divide 121 by 11 to get 11. Here, 11 is the smallest prime number that cannot be divided anymore.
So, the prime factorization of 726 is: 2 × 3 × 112.
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 726: (1, 726), (2, 363), (3, 242), (6, 121), (11, 66), and (22, 33).
Negative factor pairs of 726: (-1, -726), (-2, -363), (-3, -242), (-6, -121), (-11, -66), and (-22, -33).
Common Mistakes and How to Avoid Them in Factors of 726
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 number. Always remember to include 1 and the number itself.
For example, in factors of 726, 1 and 726 are also factors.
Factors of 726 Examples
Problem 1
There are 11 friends and 726 candies. How will they divide them equally?
They will get 66 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of friends.
726/11 = 66
Problem 2
A field is rectangular, the length of the field is 33 meters, and the total area is 726 square meters. Find the width.
22 meters.
Explanation
To find the width of the field, we use the formula: Area = length × width 726 = 33 × width
To find the value of width, we need to shift 33 to the left side.
726/33 = width
Width = 22.
Problem 3
There are 6 trucks and 726 boxes. How many boxes will be in each truck?
Each truck will have 121 boxes.
Explanation
To find the boxes in each truck, divide the total boxes by the trucks.
726/6 = 121
Problem 4
In a class, there are 726 students, and 3 groups. How many students are there in each group?
There are 242 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
726/3 = 242
Problem 5
726 books need to be arranged in 66 shelves. How many books will go on each shelf?
Each of the shelves has 11 books.
Explanation
Divide total books by shelves.
726/66 = 11
FAQs on Factors of 726
1.What are the factors of 726?
2.Mention the prime factors of 726.
3.Is 726 a multiple of 11?
4.Mention the factor pairs of 726?
5.What is the square of 726?
6.How can children in United Kingdom use numbers in everyday life to understand Factors of 726?
7.What are some fun ways kids in United Kingdom can practice Factors of 726 with numbers?
8.What role do numbers and Factors of 726 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 726 skills?
Important Glossaries for Factors of 726
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, and 726.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 11 are prime factors of 726.
- 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 726 are (1, 726), (2, 363), etc.
- Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 726 is 2 × 3 × 112.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using the multiplication method for 726 involves finding pairs like (1, 726) and (2, 363).
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About BrightChamps in United Kingdom
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.
