Factors of 120
Factors of 120 are numbers that, when multiplied in pairs give the product as 120. There are overall 16 factors of 120, of which 2, 3 and 5 are its prime factors. The Prime Factorization of 120 is 2^{3} × 3 × 5.
 Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
 Negative Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120
 Prime Factors of 120: 2, 3, 5
 Prime Factorization of 120: 2 × 2 × 2 × 3 × 5 = 2^{3} × 3 × 5
 Sum of Factors of 120: 360
1.  What Are the Factors of 120? 
2.  How to Calculate Factors of 120? 
3.  Important Notes 
4.  Factors of 120 by Prime Factorization 
5.  Factors of 120 in Pairs 
6.  Tips and Tricks 
7.  FAQs on Factors of 120 
What Are the Factors of 120?
The factors of 120 are integers that divide 120 without any remainder. For example,10 is a factor of 120 because 10 divides 120 without any remainder. Interestingly, 12, which is the quotient of the above division, is also a factor of 120. Check whether you get 0 as the remainder by dividing 120 by 12 using long division.
How to Calculate the Factors of 120?
The steps to find the factors of any number:
 Divide the number by 2 and get another number. If the resultant number is not an integer, then round it to the nearest integer.
 Divide the given number by each of the numbers from 1 to the resultant number (from step 1) and see which of them results in the remainder 0. We divide only by these numbers as any number that is greater than half of a given number cannot be its factor.
 The divisor of each such division (with remainder 0) is the factor of that number. Also, the given number is also a factor of itself.
 All the factors of 120 that divide 120 without any remainder are:
120 ÷ 1 = 120
120 ÷ 2 = 60
120 ÷ 3 = 40
120 ÷ 4 = 30
120 ÷ 5 = 24
120 ÷ 6 = 20
120 ÷ 8 = 15
120 ÷ 10 = 12
Important Notes
 Fractions and decimals that are not integers cannot be the factors of any number
 When a number is a factor of the given number, then its additive inverse is also a factor of the given number.
For example, since 8 is a factor of 120, 8 is also a factor of 120.
Factors of 120 By Prime Factorization
Let us find the prime factorization of 120 by expressing it as the product of prime numbers.
So the prime factorization of 120 is 2^{3} × 3 × 5
From the prime factorization of 120, it is clear that 2,3, and 5 are the factors of 120. In fact, 2, 3 and 5 are the prime factors of 120. Also, we know that 1 is a factor of every number. Thus, The factors of 120 by prime factorization are 1, 2, 3, 5, 15, 30, 60, and 120.
To understand the concept of finding factors by prime factorization better, let us take a few more examples.
 Factors of 256  The factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256
 Factors of 54  The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54
 Factors of 55  The factors of 55 are 1, 5, 11, and 55
 Factors of 58  The factors of 58 are 1, 2, 29, and 58
 Factors of 48  The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
Tips and Tricks
While finding the factors of a number keep the following in mind:
 1 and the number itself are always the factors of a number.
 To find the other factors of the number, we first find its prime factorization. Then, the multiplicands of the prime factorization are the prime factors of the number.
 By multiplying some or all multiplicands in different combinations, we get the composite factors of the number.
Factors of 120 in Pairs
The pair factors of 120 are obtained by writing 120 as a product of two numbers in all possible ways. In each product, both multiplicands are the factors of 120.
Product that Results in 120 
Pair Factors of 120 

1 × 120  (1, 120) 
2 × 60  (2, 60) 
3 × 40 
(3,40) 
4 × 30 
(4, 30) 
5 × 24 
(5,24) 
6 × 20 
(6,20) 
8 × 15 
(8,15) 
10 × 12 
(10,12) 
The negative pair factors of 120 are (1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), and (10,12).
Factors of 120 Solved Examples

Example 1: Andy has to find the highest common factors of 120 and 60. Help her find them.
Solution:
Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Hence, the highest common factor of 120 and 60 is 60 
Example 2 Smith has to write all the pair factors of 120 whose sum lies between 60 and 70. Help him to find the pair.
Solution:
The pair factors of 120 are, (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), (10, 12)
The sum pair factor of 120 whose sum lies between 60 and 70 is (2, 60). 
Example 3: Find the product of all the prime factors of 120.
Solution:
Since, the prime factors of 120 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.
FAQs on Factors of 120
What are the Factors of 120?
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and its negative factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
What is the Sum of the Factors of 120?
Sum of all factors of 120 = (2^{3 + 1}  1)/(2  1) × (3^{1 + 1}  1)/(3  1) × (5^{1 + 1}  1)/(5  1) = 360
What is the Greatest Common Factor of 120 and 73?
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and the factors of 73 are 1, 73. 120 and 73 have only one common factor which is 1. This implies that 120 and 73 are coprime.
Hence, the Greatest Common Factor (GCF) of 120 and 73 is 1.
What are the Prime Factors of 120?
The prime factors of 120 are 2, 3, 5.
How Many Factors of 120 are also Common to the Factors of 65?
Since, the factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 and the factors of 65 are 1, 5, 13, 65.
Hence, [1, 5] are the common factors of 120 and 65.
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