122 LearnersLast updated on May 26th, 2025
Factors of 7200
Factors are the numbers that divide any given number evenly without a 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 7200, how they are used in real life, and tips to learn them quickly.
What are the Factors of 7200?
The numbers that divide 7200 evenly are known as factors of 7200.
A factor of 7200 is a number that divides the number without remainder.
The factors of 7200 include numbers like 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 2400, 3600, and 7200.
Negative factors of 7200: The negative counterparts of the positive factors, such as -1, -2, -3, -4, etc.
Prime factors of 7200: 2, 3, and 5.
Prime factorization of 7200: 25 × 32 × 52.
The sum of factors of 7200: This is calculated by adding all the factors listed above.
How to Find Factors of 7200?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using the 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 7200. Identifying the numbers which are multiplied to get the number 7200 is the multiplication method.
Step 1: Multiply 7200 by 1, 7200 × 1 = 7200.
Step 2: Check for other numbers that give 7200 after multiplying. Examples: 2 × 3600 = 7200 3 × 2400 = 7200 4 × 1800 = 7200 Therefore, the positive factor pairs of 7200 include: (1, 7200), (2, 3600), (3, 2400), (4, 1800), etc.
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 the simple division method
Step 1: Divide 7200 by 1, 7200 ÷ 1 = 7200.
Step 2: Continue dividing 7200 by the numbers until the remainder becomes 0.
7200 ÷ 1 = 7200
7200 ÷ 2 = 3600
7200 ÷ 3 = 2400
7200 ÷ 4 = 1800
Therefore, the factors of 7200 include numbers like 1, 2, 3, 4, etc.
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 7200 divide the number to break it down in the multiplication form of prime factors until the remainder becomes 1.
7200 ÷ 2 = 3600
3600 ÷ 2 = 1800
1800 ÷ 2 = 900
900 ÷ 2 = 450
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
5 ÷ 5 = 1
The prime factors of 7200 are 2, 3, and 5.
The prime factorization of 7200 is: 25 × 32 × 52.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following steps show
Step 1: Firstly, 7200 is divided by 2 to get 3600.
Step 2: Now divide 3600 by 2 to get 1800.
Step 3: Then divide 1800 by 2 to get 900.
Step 4: Divide 900 by 2 to get 450.
Step 5: Continue dividing by the smallest prime numbers until the end, using 3 and then 5. So, the prime factorization of 7200 is: 25 × 32 × 52.
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 7200: (1, 7200), (2, 3600), (3, 2400), etc.
Negative factor pairs of 7200: (-1, -7200), (-2, -3600), (-3, -2400), etc.
Common Mistakes and How to Avoid Them in Factors of 7200
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 7200, 1 and 7200 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 7200 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions as factors. Only whole numbers can be a factor.
For example, thinking 3.5 as a factor, because 7200/3.5 ≈ 2057.14, 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 7200 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 7200, but it has other factors like 4, 6, 8, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 7200 as 25 × 32 × 52 and missing all the key factors.
Factors of 7200 Examples
Problem 1
There are 720 students and 7200 candies. How will they divide it equally?
They will get 10 candies each.
Explanation
To divide the candies equally, we need to divide the total candies by the number of students.
7200/720 = 10
Problem 2
A garden is rectangular, the length of the garden is 60 meters and the total area is 7200 square meters. Find the width.
120 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
7200 = 60 × width
To find the value of width, we need to shift 60 to the left side.
7200/60 = width
Width = 120.
Problem 3
There are 240 boxes and 7200 items. How many items will be in each box?
Each box will have 30 items.
Explanation
To find the items in each box, divide the total items by the number of boxes.
7200/240 = 30
Problem 4
In a class, there are 720 students, and 36 groups. How many students are there in each group?
There are 20 students in each group.
Explanation
Dividing the students by the total groups, we will get the number of students in each group.
720/36 = 20
Problem 5
7200 books need to be arranged in 80 shelves. How many books will go on each shelf?
Each of the shelves has 90 books.
Explanation
Divide the total books by the number of shelves.
7200/80 = 90
FAQs on Factors of 7200
1.What are the factors of 7200?
2.Mention the prime factors of 7200.
3.Is 7200 a multiple of 18?
4.Mention the factor pairs of 7200?
5.What is the square of 7200?
6.How can children in India use numbers in everyday life to understand Factors of 7200?
7.What are some fun ways kids in India can practice Factors of 7200 with numbers?
8.What role do numbers and Factors of 7200 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve Factors of 7200 skills?
Important Glossaries for Factors of 7200
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 7200 include numbers such as 1, 2, 3, 4, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 7200.
- Prime factorization: Expressing a number as a product of its prime factors. For 7200, it is 25 × 32 × 52.
- 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 7200 include (1, 7200), (2, 3600), etc.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to the original number.
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About BrightChamps in India
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.
