137 LearnersLast updated on June 4th, 2025
Factors of 720
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing the items equally, arranging things, etc. In this topic, we will learn about the factors of 720, how they are used in real life, and the tips to learn them quickly.
What are the Factors of 720?
The numbers that divide 720 evenly are known as factors of 720.
A factor of 720 is a number that divides the number without remainder.
The factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720.
Negative factors of 720: -1, -2, -3, -4, -5, -6, -8, -9, -10, -12, -15, -16, -18, -20, -24, -30, -36, -40, -45, -48, -60, -72, -80, -90, -120, -144, -180, -240, -360, and -720.
Prime factors of 720: 2, 3, and 5.
Prime factorization of 720: (24 × 32 × 5).
The sum of factors of 720: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 36 + 40 + 45 + 48 + 60 + 72 + 80 + 90 + 120 + 144 + 180 + 240 + 360 + 720 = 2418.
How to Find Factors of 720?
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 720. Identifying the numbers which are multiplied to get the number 720 is the multiplication method.
Step 1: Multiply 720 by 1, \(720 \times 1 = 720\).
Step 2: Check for other numbers that give 720 after multiplying:
\(2 \times 360 = 720\)
\(3 \times 240 = 720\)
\(4 \times 180 = 720\)
\(5 \times 144 = 720\)
\(6 \times 120 = 720\)
These are just a few examples.
Therefore, the positive factor pairs of 720 include: (1, 720), (2, 360), (3, 240), (4, 180), (5, 144), (6, 120), 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 720 by 1, \(720 \div 1 = 720\).
Step 2: Continue dividing 720 by the numbers until the remainder becomes 0.
\(720 \div 1 = 720\)
\(720 \div 2 = 360\)
\(720 \div 3 = 240\)
\(720 \div 4 = 180\)
\(720 \div 5 = 144\)
\(720 \div 6 = 120\)
Therefore, the factors of 720 include: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720.
Prime Factors and Prime Factorization
The factors can be found by dividing it with a 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 720 divide the number to break it down in the multiplication form of prime factors till the remainder becomes 1.
\(720 \div 2 = 360\)
\(360 \div 2 = 180\)
\(180 \div 2 = 90\)
\(90 \div 2 = 45\)
\(45 \div 3 = 15\)
\(15 \div 3 = 5\)
\(5 \div 5 = 1\)
The prime factors of 720 are 2, 3, and 5.
The prime factorization of 720 is: \(2^4 \times 3^2 \times 5\).
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows:
Step 1: Firstly, 720 is divided by 2 to get 360.
Step 2: Now divide 360 by 2 to get 180.
Step 3: Then divide 180 by 2 to get 90.
Step 4: Divide 90 by 2 to get 45.
Step 5: Divide 45 by 3 to get 15.
Step 6: Divide 15 by 3 to get 5. Here, 5 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 720 is: \(2^4 \times 3^2 \times 5\).
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 720: (1, 720), (2, 360), (3, 240), (4, 180), (5, 144), (6, 120), etc.
Negative factor pairs of 720: (-1, -720), (-2, -360), (-3, -240), (-4, -180), (-5, -144), (-6, -120), etc.
Common Mistakes and How to Avoid Them in Factors of 720
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 720, 1 and 720 is also a factor.
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 720 consist of -1, -2, -3, etc.
Mistake 3
Including the Fraction
Children might sometimes add fractions also as a factor. Only whole numbers can be a factor.
For example, thinking 1.5 as a factor, because 720/1.5 = 480, 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 720 are prime numbers.
For example, 2, 3, and 5 are the prime factors of 720, but it has other factors like 4, 6, 9, etc.
Mistake 5
Mistake in Factorization
Children might skip the steps in factorization and end up writing wrong factors.
For example, not breaking 720 as \(2^4 \times 3^2 \times 5\) and missing all the key factors.
Factors of 720 Examples
Problem 1
There are 9 students and 720 pencils. How will they divide them equally?
They will get 80 pencils each.
Explanation
To divide the pencils equally, we need to divide the total pencils with the number of students.
720/9 = 80
Problem 2
A rectangular garden has a length of 24 meters and a total area of 720 square meters. Find the width.
30 meters.
Explanation
To find the width of the garden, we use the formula,
Area = length × width
720 = 24 × width
To find the value of width, we need to shift 24 to the left side.
720/24 = width
Width = 30.
Problem 3
There are 45 baskets and 720 apples. How many apples will be in each basket?
Each basket will have 16 apples.
Explanation
To find the apples in each basket, divide the total apples with the baskets.
720/45 = 16
Problem 4
In a company, there are 720 employees, and 8 departments. How many employees are there in each department?
There are 90 employees in each department.
Explanation
Dividing the employees with the total departments, we will get the number of employees in each department.
720/8 = 90
Problem 5
720 chairs need to be arranged in 6 rows. How many chairs will go in each row?
Each of the rows has 120 chairs.
Explanation
Divide total chairs with rows.
720/6 = 120
FAQs on Factors of 720
1.What are the factors of 720?
2.Mention the prime factors of 720.
3.Is 720 a multiple of 6?
4.Mention the factor pairs of 720?
5.What is the square of 720?
6.How can children in United States use numbers in everyday life to understand Factors of 720?
7.What are some fun ways kids in United States can practice Factors of 720 with numbers?
8.What role do numbers and Factors of 720 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Factors of 720 skills?
Important Glossaries for Factors of 720
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 720 are 1, 2, 3, 4, 5, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, and 5 are prime factors of 720.
- 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 720 are (1, 720), (2, 360), etc.
- Prime factorization: The expression of a number as the product of its prime factors. For example, the prime factorization of 720 is \(2^4 \times 3^2 \times 5\).
- Negative factors: Negative numbers that divide the given number without leaving a remainder. For example, -1, -2, -3, -4, etc., are negative factors of 720.
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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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