Factors of 120 – Easy Division & Prime Factorization

Factors Of 120

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

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, those 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.

Below are some positive and negative pair factors of 120.

Likewise, the negative pair factors of 120 are:

Prime Factorization of 120

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

• 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.

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.

Factors of 121= 1, 11, and 121.

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

Example 2:

Calculate 38 and 75’s common factors.

Solution:

Factors of 38 = 1, 2, 19, and 38.

All 75 factor= 1, 3, 5, 15, 25, and 75.

Thus, the common factor of 38 and 75 is 1.

Example 3:

Calculate the common factors of 120 and 24.

Solution:

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

Factors of 24= 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore, the common factors of 120 and 24 are 1, 2, 3, 4, 6, 12, and 24.

FAQ`s