# Factors of 180

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180

#### How to find factors of a number

 1.   Find factors of 180 using Division Method 2.   Find factors of 180 using Prime Factorization 3.   Find factors of 180 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 180

• Divide 180 by 1: 180 ÷ 1 : Remainder = 0
• Divide 180 by 2: 180 ÷ 2 : Remainder = 0
• Divide 180 by 3: 180 ÷ 3 : Remainder = 0
• Divide 180 by 4: 180 ÷ 4 : Remainder = 0
• Divide 180 by 5: 180 ÷ 5 : Remainder = 0
• Divide 180 by 6: 180 ÷ 6 : Remainder = 0
• Divide 180 by 9: 180 ÷ 9 : Remainder = 0
• Divide 180 by 10: 180 ÷ 10 : Remainder = 0
• Divide 180 by 12: 180 ÷ 12 : Remainder = 0
• Divide 180 by 15: 180 ÷ 15 : Remainder = 0
• Divide 180 by 18: 180 ÷ 18 : Remainder = 0
• Divide 180 by 20: 180 ÷ 20 : Remainder = 0
• Divide 180 by 30: 180 ÷ 30 : Remainder = 0
• Divide 180 by 36: 180 ÷ 36 : Remainder = 0
• Divide 180 by 45: 180 ÷ 45 : Remainder = 0
• Divide 180 by 60: 180 ÷ 60 : Remainder = 0
• Divide 180 by 90: 180 ÷ 90 : Remainder = 0
• Divide 180 by 180: 180 ÷ 180 : Remainder = 0

Hence, Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180

#### 2. Steps to find factors of 180 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 180 using the division method, follow these steps:

• Step 1. Start dividing 180 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 180, which is 2. Divide 180 by 2 to obtain the quotient (90).
180 ÷ 2 = 90
• Step 3. Repeat step 1 with the obtained quotient (90).
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 180 is, 180 = 2 x 2 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 180 as shown below:

So, the prime factorization of 180 is, 180 = 2 x 2 x 3 x 3 x 5.

#### 3. Find factors of 180 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 180 would be the two numbers which, when multiplied, give 180 as the result.

The following table represents the calculation of factors of 180 in pairs:

Factor Pair Pair Factorization
1 and 180 1 x 180 = 180
2 and 90 2 x 90 = 180
3 and 60 3 x 60 = 180
4 and 45 4 x 45 = 180
5 and 36 5 x 36 = 180
6 and 30 6 x 30 = 180
9 and 20 9 x 20 = 180
10 and 18 10 x 18 = 180
12 and 15 12 x 15 = 180

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 180. They are called negative pair factors.

Hence, the negative pairs of 180 would be ( -1 , -180 ) , ( -2 , -90 ) , ( -3 , -60 ) , ( -4 , -45 ) , ( -5 , -36 ) , ( -6 , -30 ) , ( -9 , -20 ) , ( -10 , -18 ) and ( -12 , -15 ) .

#### 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. 180 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 180.
• Every number is a factor of zero (0), since 180 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, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are exact divisors of 180.
• Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. Each factor divides 180 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180 are all less than or equal to 180.

• Which is the smallest prime factor of 180?

Smallest prime factor of 180 is 2.

• Is 180 a perfect square?

No 180 is not a perfect square.

• What are five multiples of 180?

First five multiples of 180 are 360, 540, 720, 900, 1080.

• What is prime factorization of 180?

Prime factorization of 180 is 2 x 2 x 3 x 3 x 5.

• What are factors of 180?

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.

• How do you find factors of a negative number? ( eg. -180 )?

Factors of -180 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, -180.

• Is 180 a whole number?

Yes 180 is a whole number.

• Which is greatest factor of 180?

The greatest factor of 180 is 90.

• What are the prime factors of 180?

The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Prime factors of 180 are 2, 2, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 180. Can you help her?

Prime factors of 180 are 2, 2, 3, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 180?

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Even factors of 180 are 2, 4, 6, 10, 12, 18, 20, 30, 36, 60, 90, 180.
Hence, product of even factors of 180 is; 2 x 4 x 6 x 10 x 12 x 18 x 20 x 30 x 36 x 60 x 90 x 180 = 2176782336000000.

Joy wants to calculate mean of all the factors of 180. Help him in finding the mean of 180.

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 180 is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 30 + 36 + 45 + 60 + 90 + 180 = 546.
Hence, the mean of factors of 180 is 546 ÷ 18 = 30.33.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 180? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -30, -36, -45, -60, -90, -180.

How many factors are there for 180?

Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
So there are in total 18 factors.

Joey wants to write all the prime factors of 180 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 180 are 2, 2, 3, 3, 5.
So in exponential form it can be written as 22 x 32 x 5.

Kevin has been asked to write 17 factor(s) of 180. Can you predict the answer?

17 factor(s) of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90.