Factors of 120—with division and prime factorization

Factors of 120

Factors Of 120

The factors of 120 are the pair of numbers, multiplied together, which gives the result 120.

 Mathematicians can use many factors in their calculations, such as factors of 56, 90, etc. The prime factors of number 120 produce the prime numbers. We will use the division method to find the factors of 120. We will now find the factors in pairs, the total factors, and the prime factorization of 120.

What are the Factors of 120?

The factors of 120 are the numbers that divide 120 exactly without leaving any remainders. Therefore, the numbers that, when multiplied in pairs, resulting in the original number 120, are called factors of 120. Since 120 is a composite number, it has more than two factors. 

Factors of 120

There are 120 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Factors of 120: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Prime Factorization of 120: 23×3×5 

 What are the Factors of -120?

When we multiply two numbers, and we get -120 as a product, that numbers are the factors of -120. 

Here is the explanation:


-1 × 120 = -120

 1 ×  -120 = -120 

-2 ×  60 = -120

 2 ×  -60 = -120 

-3 ×  40 = -120

 3 ×  -40 = -120

 -4 × 30 = -120 

4 ×  -30 = -120 

-5 × 24 = -120  

5 ×  -24 = -120 

6 × 20 = -120 

6 ×  -20 = -120 

 -8 × 20 = -120 

8 × -20 = -120  

-10 × 12 = -120 

10 ×  -12 = -120



We can get -120 by having (-1, 120), (-2, 60), (-3, 40), (-4, 30), (-5, 24), (-6, 20), (-8, 15), and (-10, 12) as a pair of factors. Similarly, we can also get -120 by having  (1, -120), (2, -60), (3, -40), (4, -30), (5, -24), (6, -20), (8, -15), and (10, -12)as a pair of factor

Pair Factors of 120

When we multiply two numbers in a pair to get the original number, we can find the pair factors of the number 120. It is possible that pair factors of 120 can be positive or negative.

Factors of 120 in pairs

Below are some positive and negative pair factors of 120.

Positive Factors of 120Positive 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)

Likewise, the negative pair factors of 120 are:

Negative Factors of 120Negative 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)

Prime Factorization of 120

A composite number is 120. We can now find the prime factors of 120.

Factors of 120 by prime factorization
  • As a first step, divide the number 120 by the smallest prime factor, which is 2, and keep dividing by 2 until you arrive at a fraction.

120 ÷ 2 = 60

60 ÷ 2 = 30

30 ÷ 2 = 15

15 ÷ 2 = 7.5; 7.5 cannot be a factor

  • Next, divide 3 by a fraction or 1 and move on to the next prime number, 3.

15 ÷ 3 = 5

5 ÷ 3 = 1.66; cannot be a factor

  • Therefore, we move on to the next prime number, 5.

5 ÷ 5 = 1

As a result of the division process, we received a 1, and we cannot proceed. Therefore, 120 has prime factors in the range of 2 × 2 × 2 × 2 × 3 × 5 or 23 × 3 × 5, where 2, 3, and 5 are prime numbers.

Links Related to Factors
Factors of 15= 1, 3, 5, and 15.Factors of 36= 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Factors of 48= 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.Factors of 18= 1, 2, 3, 6, 9 and 18.
Factors of 42= 1, 2, 3, 6, 7, 14, 21, and 42.Factors of 60= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 35= 1, 5, 7, and 35.Factors of 72= 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 84= 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84.Factors of 50= 1, 2, 5, 10, 25, 50.

Solved Examples

Example1:

Calculate the common factors of 120 and 121.

Solution:

There are 120 factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

121 has the factors 1, 11 and 121.

As a result, 120 and 121 share a common factor of 1.

Example 2:

Calculate 120 and 119’s common factors.

Solution:

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120

Factors of 119 = 1, 7, 17, 119.

Thus, the common factor of 120 and 119 is 1.

Example 3:

Calculate the common factors of 120 and 60.

Solution:

The factors of 120 are 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.

Therefore, the common factors of 120 and 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

FAQ`s

What are the factors of 120?

Factors of 120 are the numbers that are multiplied in pairs to give the original number 120.

Factors of 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.

What is the prime factorization of 120?

Prime factorization of 120 = 2 × 2 × 2 × 3 × 5 or 23 × 3 × 5.

What are the positive pair factors of 120?

These are the positive pair factors of 120: (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), and (10, 12).

Write down the negative pair factors of 120?

These are the negative pair factors of 120: (-1, -120), (-2, -60), (-3, -40), (-4, -30), (-5, -24), (-6, -20), (-8, -15), and (-10, -12).

Is 60 a factor of 120?

It is true that 60 is a factor of 120. Due to the fact that 60 divides 120 exactly without leaving any remainder, 60 is a factor of 120.

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