# Factors of 120

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

#### How to find factors of a number

 1.   Find factors of 120 using Division Method 2.   Find factors of 120 using Prime Factorization 3.   Find factors of 120 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 120

• Divide 120 by 1: 120 ÷ 1 : Remainder = 0
• Divide 120 by 2: 120 ÷ 2 : Remainder = 0
• Divide 120 by 3: 120 ÷ 3 : Remainder = 0
• Divide 120 by 4: 120 ÷ 4 : Remainder = 0
• Divide 120 by 5: 120 ÷ 5 : Remainder = 0
• Divide 120 by 6: 120 ÷ 6 : Remainder = 0
• Divide 120 by 8: 120 ÷ 8 : Remainder = 0
• Divide 120 by 10: 120 ÷ 10 : Remainder = 0
• Divide 120 by 12: 120 ÷ 12 : Remainder = 0
• Divide 120 by 15: 120 ÷ 15 : Remainder = 0
• Divide 120 by 20: 120 ÷ 20 : Remainder = 0
• Divide 120 by 24: 120 ÷ 24 : Remainder = 0
• Divide 120 by 30: 120 ÷ 30 : Remainder = 0
• Divide 120 by 40: 120 ÷ 40 : Remainder = 0
• Divide 120 by 60: 120 ÷ 60 : Remainder = 0
• Divide 120 by 120: 120 ÷ 120 : Remainder = 0

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

#### 2. Steps to find factors of 120 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 120 using the division method, follow these steps:

• Step 1. Start dividing 120 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 120, which is 2. Divide 120 by 2 to obtain the quotient (60).
120 ÷ 2 = 60
• Step 3. Repeat step 1 with the obtained quotient (60).
60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 120 is, 120 = 2 x 2 x 2 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 120 as shown below:

So, the prime factorization of 120 is, 120 = 2 x 2 x 2 x 3 x 5.

#### 3. Find factors of 120 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 120 would be the two numbers which, when multiplied, give 120 as the result.

The following table represents the calculation of factors of 120 in pairs:

Factor Pair Pair Factorization
1 and 120 1 x 120 = 120
2 and 60 2 x 60 = 120
3 and 40 3 x 40 = 120
4 and 30 4 x 30 = 120
5 and 24 5 x 24 = 120
6 and 20 6 x 20 = 120
8 and 15 8 x 15 = 120
10 and 12 10 x 12 = 120

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 120. They are called negative pair factors.

Hence, the negative pairs of 120 would be ( -1 , -120 ) , ( -2 , -60 ) , ( -3 , -40 ) , ( -4 , -30 ) , ( -5 , -24 ) , ( -6 , -20 ) , ( -8 , -15 ) and ( -10 , -12 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 120 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 120.
• Every number is a factor of zero (0), since 120 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are exact divisors of 120.
• Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. Each factor divides 120 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 are all less than or equal to 120.

• What are the prime factors of 120?

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

• What two numbers make 120?

Two numbers that make 120 are 2 and 60.

• What is the greatest prime factors of 120?

The greatest prime factor of 120 is 5.

• What are factors of 120?

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

• How do you find factors of a negative number? ( eg. -120 )?

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

• What are five multiples of 120?

First five multiples of 120 are 240, 360, 480, 600, 720.

• Write some multiples of 120?

First five multiples of 120 are 240, 360, 480, 600.

• Is 120 a perfect square?

No 120 is not a perfect square.

• What two numbers make 120?

Two numbers that make 120 are 2 and 60.

#### Examples of Factors

What is prime factorization of 120?

Prime factorization of 120 is 2 x 2 x 2 x 3 x 5 = 23 x 3 x 5.

Sammy is puzzled while calculating the prime factors of 120. Can you help him find them?

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

Kevin has been asked to write 15 factor(s) of 120. Can you predict the answer?

15 factor(s) of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60.

Joey wants to write all the prime factors of 120 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 120 are 2, 2, 2, 3, 5.
So in exponential form it can be written as 23 x 3 x 5.

How many factors are there for 120?

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
So there are in total 16 factors.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 120? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Negative factors are -1, -2, -3, -4, -5, -6, -8, -10, -12, -15, -20, -24, -30, -40, -60, -120.

Can you help Rubel to find out the product of the even factors of 120?

Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Even factors of 120 are 2, 4, 6, 8, 10, 12, 20, 24, 30, 40, 60, 120.
Hence, product of even factors of 120 is; 2 x 4 x 6 x 8 x 10 x 12 x 20 x 24 x 30 x 40 x 60 x 120 = 191102976000000.