Factors of 120

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 itself. These factors are the values by which 120 can be divided without producing a remainder. Not only the set of positive integers but also negative integers that divide 120 evenly are the factors of 120.

In this article, we will learn what are the factors of 120, how to find factors of 120, and factor pairs of 120 in detail.

What are Factors of 120?

Factors of 120 are the integers that divide 120 without producing a remainder. for instance, 6 is a factor of 120 since, upon dividing 120 by 6, the residue is equal to 0. Furthermore, 20 is a factor of 120 as well. Now, let's multiply some of the integers pairwise to obtain 120:

• 1 × 120 = 120
• 2 × 60 = 120
• 3 × 40 = 120
• 4 × 30 = 120
• 5 × 24 = 120
• 6 × 20 = 120
• 8 × 15 = 120
• 10 × 12 = 120

So, each pair represents the factors of 120, and that are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.

Factor of 120 Calculator

Try out the following calculator to find the factors of 120

How to Find Factors of 120?

Factors of 120, can be resolved by various methods;

• Multiplication Method
• Division Method

Factors of 120 using Multiplication Method

By combining two factors so that their total multiplicative power equals 120, you can find the factors of 120 using the multiplication method. So, Check out the paring of integers and reach 120.

• 1 × 120 = 120
• 2 × 60 = 120
• 3 × 40 = 120
• 4 × 30 = 120
• 5 × 24 = 120.... So on

So, the factors of 120 are 1, 2, 3, 4, 5, 24, 30, 40, 60, and 120 is proven by the multiplication method.

Factors of 120 using Division Method

To get the factors of 120, you can divide 120 by increasing numbers starting at 1 and working your way up to 120. So, Let's examine how two numbers are paired together;

• 120 ÷ 1 = 120
• 120 ÷ 2 = 60
• 120 ÷ 3 = 40
• 120 ÷ 4 = 30
• 120 ÷ 5 = 24
• 120 ÷ 6 = 20... So on

So, the factors of 120 are 1, 2, 3, 4, 5,6,20, 24, 30, 40, 60, and 120 is proven by the Division method.

All Factors of 120

Here is a list of all the factors of 120:

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

Prime Factorization of 120

The number 120 is a composite number that consists of more than two factors. To find the prime factors or prime factorization of 120 some steps should be followed;

• Start with the number itself 120

• Then, let's divide 120 by the smallest prime factor 2, 120 ÷ 2 = 60

• After that, continuing factorization of 60, 60 ÷ 2 = 30

• Then, Continue factoring the quotient 30, 30 ÷ 2 = 15

• Now, 15 can't be divided by 2, so the next prime will be 3,15 ÷ 3 = 5

• At last, we get the prime number which is 5.

Therefore, prime factorization of 120 are 2 × 2 × 2 × 3 × 5 or 2³ × 3 × 5

Prime Factors of 120

As we have seen the prime factorization of 120 is given as;

120 = 2³ × 3 × 5

Hence, the Prime factor of 120 is 2 which is raised to power 3,3, and 5.

Learn, Prime Factorization

Factor Tree of 120

Here, the factor tree 120 is given below in the following steps;

• Start with 120

• Divide by the smallest prime factor, which is 2

• 2 is the prime number that remains as it is, 60 splits into two factors 2 and 30

• Then again, 2 will remain as it is, 30 splits into 2 and 15

• At last, 2 remain the same as above and 15 splits into two factors 3 and 5

Now you get the factors tree of 120, that is 2³ × 3 × 5

Factor tree of 120 is shown below:

Factor Pairs of 120

A number's factor pair is a collection of two factors multiplied by the number itself. For example: 2 × 60 is the factor pair of 120. So, for more example let's see the positive pair factors and the negative pair factors of 160;

Positive Factor Pairs of 120

Positive Factor Pairs of 120 are tabulated below;

Negative Factor Pairs of 120

Negative Factor Pairs of 120 are tabulated below;

Also, Check

• Factors of 12
• Factors of 20
• Factors of 10

Solved Examples on Factors of 120

Example 1: Calculate the Sum of all the factors of 120.

Solution:

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

Sum = 1 + 2 + 3 + 4 + 5 + 6 + 8 + 10 + 12 + 15 + 20 + 24 + 30 + 40 + 60 + 120 = 360

Therefore , sum of all factors of 120 is 360

Example 2: List the common factors between 40, and 120.

Solution:

Common factors between 40, 120 are:

40 = 1, 2, 4, 5, 8, 10, 20, 40

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

Therefore, common factors between 40, and 120 are 1, 2, 4, 5, 8, 10, 20, and 40

Example 3: List the common factors between 60, and 120.

Solution:

Common factors between 60, 120 are:

60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

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

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

Example 4: Find the greatest common factor of 93 and 120.

Solution:

93 = 3 × 31

120 = 2³ ×3 × 5

Greatest Common Factor of 93 and 120 is 3

Practice Questions on Factors of 120

Q1: Determine if 15 is a factor of 120.

Q2: Use the division method to find the factors of 120.

Q3: Identify the common factors of 120 and 150.

Q4: Express 120 as the product of its prime factors.

Q5: Determine if 10 is a factor of 120.

Q6: What is the greatest common factor (GCF) of 120 and 80?

Q7: List all the pairs of factors of 120.

Q8: How many even factors does 120 have?

Q9: Is 24 a factor of 120? Justify your answer.

Q10: If a number is a factor of 120. what can you say about its divisibility by 3?

Conclusion

The factors of 120 are the integers that can be multiplied in pairs to the produce the number 120. The complete list of the factors includes 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120. Understanding the factors of the number is essential for the various applications in the mathematics including the simplifying fractions and finding greatest common divisors. The factors also help in analyzing the properties of numbers in the number theory.