102 LearnersLast updated on May 26th, 2025
Factors of 724
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 724, how they are used in real life, and tips to learn them quickly.
What are the Factors of 724?
The numbers that divide 724 evenly are known as factors of 724.
A factor of 724 is a number that divides the number without remainder.
The factors of 724 are 1, 2, 4, 181, 362, and 724.
Negative factors of 724: -1, -2, -4, -181, -362, and -724.
Prime factors of 724: 2 and 181.
Prime factorization of 724: 2² × 181.
The sum of factors of 724: 1 + 2 + 4 + 181 + 362 + 724 = 1274
How to Find Factors of 724?
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 724. Identifying the numbers that are multiplied to get the number 724 is the multiplication method.
Step 1: Multiply 724 by 1, 724 × 1 = 724.
Step 2: Check for other numbers that give 724 after multiplying
2 × 362 = 724
4 × 181 = 724
Therefore, the positive factor pairs of 724 are: (1, 724), (2, 362), and (4, 181).
All these factor pairs result in 724.
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 that result as whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 724 by 1, 724 ÷ 1 = 724.
Step 2: Continue dividing 724 by the numbers until the remainder becomes 0.
724 ÷ 1 = 724
724 ÷ 2 = 362
724 ÷ 4 = 181
Therefore, the factors of 724 are: 1, 2, 4, 181, 362, 724.
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 724 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
724 ÷ 2 = 362
362 ÷ 2 = 181
181 ÷ 181 = 1
The prime factors of 724 are 2 and 181.
The prime factorization of 724 is: 2² × 181.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 724 is divided by 2 to get 362.
Step 2: Now divide 362 by 2 to get 181. Step 3: Here, 181 is a prime number and cannot be divided further.
So, the prime factorization of 724 is: 2² × 181.
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 724: (1, 724), (2, 362), (4, 181).
Negative factor pairs of 724: (-1, -724), (-2, -362), (-4, -181).
Common Mistakes and How to Avoid Them in Factors of 724
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 724, 1 and 724 are also factors.
Factors of 724 Examples
Problem 1
There are 4 teams and 724 apples. How will they divide it equally?
They will get 181 apples each.
Explanation
To divide the apples equally, we need to divide the total apples with the number of teams.
724/4 = 181
Problem 2
A rectangular field has a width of 2 meters and a total area of 724 square meters. Find the length?
362 meters.
Explanation
To find the length of the field, we use the formula,
Area = length × width
724 = length × 2
To find the value of length, we need to shift 2 to the left side.
724/2 = length
Length = 362.
Problem 3
There are 362 bags and 724 candies. How many candies will be in each bag?
Each bag will have 2 candies.
Explanation
To find the candies in each bag, divide the total candies with the bags.
724/362 = 2
Problem 4
In a class, there are 724 students, and 181 groups. How many students are there in each group?
There are 4 students in each group.
Explanation
Dividing the students with the total groups, we will get the number of students in each group.
724/181 = 4
Problem 5
724 books need to be arranged on 2 shelves. How many books will go on each shelf?
Each of the shelves has 362 books.
Explanation
Divide total books by shelves.
724/2 = 362
FAQs on Factors of 724
1.What are the factors of 724?
2.Mention the prime factors of 724.
3.Is 724 a multiple of 4?
4.Mention the factor pairs of 724?
5.What is the square of 724?
6.How can children in Australia use numbers in everyday life to understand Factors of 724?
7.What are some fun ways kids in Australia can practice Factors of 724 with numbers?
8.What role do numbers and Factors of 724 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve Factors of 724 skills?
Important Glossaries for Factors of 724
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 724 are 1, 2, 4, 181, 362, and 724.
- Prime factors: Factors that are prime numbers. For example, 2 and 181 are prime factors of 724.
- 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 724 are (1, 724), (2, 362), etc.
- Prime factorization: The process of expressing a number as a product of its prime factors. For example, the prime factorization of 724 is 2² × 181.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number.
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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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