Factors of 720
Did you know that 720 is the only even composite number having 30 factors? In this chapter, we will calculate the factors of 720, prime factors of 720, and factors of 720 in pairs along with solved examples and interactive questions for a better understanding.
 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 Factorization of 720: 720 = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 2^{4} × 3^{2} × 5
1.  What Are the Factors of 720? 
2.  How to Calculate Factors of 720? 
3.  Factors of 720 by Prime Factorization 
4.  Factors of 720 in Pairs 
5.  FAQs on Factors of 720 
What Are the Factors of 720?
All the numbers whose product results in 720 are referred as the factors of 720. The numbers which divide 720 without leaving any remainder are the factors of 720. Hence, when any two whole numbers are multiplied with each other and 720 is obtained as the answer, both these numbers are said to be the factors of 720.
How to Calculate the Factors of 720?
The factors of 720 are calculated by determining all the numbers which would divide 720 without leaving any remainder. Hence, the divisors as well as their quotients are the factors of 720.
Numbers Dividing 720  Factors of 720 

720/1 = 720  1 and 720 are factors of 720. 
720/2 = 360  2 and 360 are factors of 720. 
720/3 = 240  3 and 240 are factors of 720. 
720/4 = 180  4 and 180 are factors of 720. 
720/5 = 144  5 and 144 are factors of 720. 
720/6 = 120  6 and 120 are factors of 720. 
720/8 = 90  8 and 90 are factors of 720. 
720/9 = 80  9 and 80 are factors of 720. 
720/10 = 72  10 and 72 are factors of 720. 
720/12 = 60  12 and 60 are factors of 720. 
720/15 = 48  15 and 48 are factors of 720. 
720/16 = 45  16 and 45 are factors of 720. 
720/18 = 40  18 and 40 are factors of 720. 
720/20 = 36  20 and 36 are factors of 720. 
720/24 = 30  24 and 30 are factors of 720. 
Hence, 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.
Explore factors using illustrations and interactive examples.
 Factors of 360  The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
 Factors of 270  The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 27, 54, 135, and 270.
 Factors of 216  The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
 Factors of 180  The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
 Factors of 91  The factors of 91 are 1, 7, 13, and 91.
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 720 by Prime Factorization
Prime factorization of 720 is expressing 720 as the product of its prime factors. To get the prime factorization of 720, we can use two methods:
 Method 1: Factor Tree Method
 Method 2: UpsideDown Division Method
Method 1: Factor Tree Method
Factor tree of 720 is:
Method 2: UpsideDown Division Method
On divding 720 by its smallest prime factor which is 2, we get
720/2 = 360
Then 360 is divided by its smallest prime factor and the quotient is obtained. This process is repeated till we get the quotient as 1.
The prime factorization of 720:
Hence, the prime factors of 720 are 2, 3, and 5.
The prime factorization of 720 is 2 × 2 × 2 × 2 × 3 × 3 × 5.
Factors of 720 in Pairs
Pairs of numbers whose product gives 720, are known as the factor pairs of 720. Let's observe the following table having factors of 720 in pairs. We consider negative integers as the negative pair factors as product of two negative integers always results in a positive integer (  ve ×  ve ) = +ve.
Positive Pair Factors of 720  Negative Pair Factors of 720 

(1, 720)  (1, 720) 
(2, 360)  (2, 360) 
(3, 240)  (3, 240) 
(4, 180)  (4, 180) 
(5, 144)  (5, 144) 
(6, 120)  (6, 120) 
(8, 90)  (8, 90) 
(9, 80)  (9, 80) 
(10, 72)  (10, 72) 
(12, 60)  (12, 60) 
(15, 48)  (15, 48) 
(16, 45)  (16, 45) 
(18, 40)  (18, 40) 
(20, 36)  (20, 36) 
(24, 30)  (24, 30) 
Important Notes:
 The sum of the digits of 720 is 9. As 9 is divisible by 3, 3 is one of the factors of 720.
 720 is not a perfect square number. Thus, it has an even number of factors.
Factors of 720 Solved Examples

Example 1: Matilda has to write all the pair factors of 720 whose sum lies between 100 and 200. Help her find them.
Solution:
The pair factors of 720 are (1, 720), (2, 360), (3, 240), (4, 180), (5, 144), (6, 120), (8, 90), (9, 80), (10, 72), (12, 60), (15, 48), (16, 45), (18, 40), (20, 36), and (24, 30).
The pair factors of 720 whose sum lies between 100 and 200 are, (4, 180), (5, 144), (6, 120), and (8, 90). 
Example 2: Can you find the factors of 720 whose pair factor contains a perfect square as one of its pair factors and their difference is an odd number.
Solution:
We know pair factors of 720 are (1, 720), (2, 360), (3, 240), (4, 180), (5, 144), (6, 120), (8, 90), (9, 80), (10, 72), (12, 60), (15, 48), (16, 45), (18, 40), (20, 36), and (24, 30).
The pair factors containing a perfect square are (4, 180), (5, 144), (9, 80), (16, 45) and (20, 36). The difference of the pair factors are 172, 139, 71, 29, and 16.Hence, the factors of 720 whose pair factor contains a perfect square as one of its pair factors and their difference is an odd number are (5, 144), (9, 80), and (16, 45).
FAQs on Factors of 720
What are the factors of 720?
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.
What are the prime factors of 720?
The prime factors of 720 are 2, 3, and 5.
Which factors of 720 are perfect squares?
The factors of 720 which are perfect squares are 1, 4, 9, 16, 36, and 144.
What are the common factors of 720 and 320?
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.
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320.
Hence, the common factors of 720 and 320 are 1, 2, 4, 5, 8, 10, 20, 40, and 80.
What are the negative pair factors of 720?
The negative pair factors of 720 are (1, 720), (2, 360), (3, 240), (4, 180), (5, 144), (6, 120), (8, 90), (9, 80), (10, 72), (12, 60), (15, 48), (16, 45), (18, 40), (20, 36), and (24, 30).
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