Last updated on June 4th, 2025
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.
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.
Factors can be found using different methods. Mentioned below are some commonly used methods:
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.
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.
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: 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: \(2^4 \times 3^2 \times 5\).
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.
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
There are 9 students and 720 pencils. How will they divide them equally?
They will get 80 pencils each.
To divide the pencils equally, we need to divide the total pencils with the number of students.
720/9 = 80
A rectangular garden has a length of 24 meters and a total area of 720 square meters. Find the width.
30 meters.
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.
There are 45 baskets and 720 apples. How many apples will be in each basket?
Each basket will have 16 apples.
To find the apples in each basket, divide the total apples with the baskets.
720/45 = 16
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.
Dividing the employees with the total departments, we will get the number of employees in each department.
720/8 = 90
720 chairs need to be arranged in 6 rows. How many chairs will go in each row?
Each of the rows has 120 chairs.
Divide total chairs with rows.
720/6 = 120
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.
: She loves to read number jokes and games.