# Factors of 540

Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, and 540

#### How to find factors of a number

 1.   Find factors of 540 using Division Method 2.   Find factors of 540 using Prime Factorization 3.   Find factors of 540 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 540

• Divide 540 by 1: 540 ÷ 1 : Remainder = 0
• Divide 540 by 2: 540 ÷ 2 : Remainder = 0
• Divide 540 by 3: 540 ÷ 3 : Remainder = 0
• Divide 540 by 4: 540 ÷ 4 : Remainder = 0
• Divide 540 by 5: 540 ÷ 5 : Remainder = 0
• Divide 540 by 6: 540 ÷ 6 : Remainder = 0
• Divide 540 by 9: 540 ÷ 9 : Remainder = 0
• Divide 540 by 10: 540 ÷ 10 : Remainder = 0
• Divide 540 by 12: 540 ÷ 12 : Remainder = 0
• Divide 540 by 15: 540 ÷ 15 : Remainder = 0
• Divide 540 by 18: 540 ÷ 18 : Remainder = 0
• Divide 540 by 20: 540 ÷ 20 : Remainder = 0
• Divide 540 by 27: 540 ÷ 27 : Remainder = 0
• Divide 540 by 30: 540 ÷ 30 : Remainder = 0
• Divide 540 by 36: 540 ÷ 36 : Remainder = 0
• Divide 540 by 45: 540 ÷ 45 : Remainder = 0
• Divide 540 by 54: 540 ÷ 54 : Remainder = 0
• Divide 540 by 60: 540 ÷ 60 : Remainder = 0
• Divide 540 by 90: 540 ÷ 90 : Remainder = 0
• Divide 540 by 108: 540 ÷ 108 : Remainder = 0
• Divide 540 by 135: 540 ÷ 135 : Remainder = 0
• Divide 540 by 180: 540 ÷ 180 : Remainder = 0
• Divide 540 by 270: 540 ÷ 270 : Remainder = 0
• Divide 540 by 540: 540 ÷ 540 : Remainder = 0

Hence, Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, and 540

#### 2. Steps to find factors of 540 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 540 using the division method, follow these steps:

• Step 1. Start dividing 540 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 540, which is 2. Divide 540 by 2 to obtain the quotient (270).
540 ÷ 2 = 270
• Step 3. Repeat step 1 with the obtained quotient (270).
270 ÷ 2 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 540 is, 540 = 2 x 2 x 3 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 540 as shown below:

So, the prime factorization of 540 is, 540 = 2 x 2 x 3 x 3 x 3 x 5.

#### 3. Find factors of 540 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 540 would be the two numbers which, when multiplied, give 540 as the result.

The following table represents the calculation of factors of 540 in pairs:

Factor Pair Pair Factorization
1 and 540 1 x 540 = 540
2 and 270 2 x 270 = 540
3 and 180 3 x 180 = 540
4 and 135 4 x 135 = 540
5 and 108 5 x 108 = 540
6 and 90 6 x 90 = 540
9 and 60 9 x 60 = 540
10 and 54 10 x 54 = 540
12 and 45 12 x 45 = 540
15 and 36 15 x 36 = 540
18 and 30 18 x 30 = 540
20 and 27 20 x 27 = 540

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 540. They are called negative pair factors.

Hence, the negative pairs of 540 would be ( -1 , -540 ) , ( -2 , -270 ) , ( -3 , -180 ) , ( -4 , -135 ) , ( -5 , -108 ) , ( -6 , -90 ) , ( -9 , -60 ) , ( -10 , -54 ) , ( -12 , -45 ) , ( -15 , -36 ) , ( -18 , -30 ) and ( -20 , -27 ) .

#### 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. 540 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 540.
• Every number is a factor of zero (0), since 540 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, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 are exact divisors of 540.
• Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540. Each factor divides 540 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, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 are all less than or equal to 540.

• Which is the smallest prime factor of 540?

Smallest prime factor of 540 is 2.

• Is 540 a perfect square?

No 540 is not a perfect square.

• What are five multiples of 540?

First five multiples of 540 are 1080, 1620, 2160, 2700, 3240.

• What is prime factorization of 540?

Prime factorization of 540 is 2 x 2 x 3 x 3 x 3 x 5.

• What are factors of 540?

Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.

• How do you find factors of a negative number? ( eg. -540 )?

Factors of -540 are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -90, -108, -135, -180, -270, -540.

• Is 540 a whole number?

Yes 540 is a whole number.

• Which is greatest factor of 540?

The greatest factor of 540 is 270.

• What are the prime factors of 540?

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
Prime factors of 540 are 2, 2, 3, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 540. Can you help her?

Prime factors of 540 are 2, 2, 3, 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 540?

Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
Even factors of 540 are 2, 4, 6, 10, 12, 18, 20, 30, 36, 54, 60, 90, 108, 180, 270, 540.
Hence, product of even factors of 540 is; 2 x 4 x 6 x 10 x 12 x 18 x 20 x 30 x 36 x 54 x 60 x 90 x 108 x 180 x 270 x 540 = 1.8509302102818816e+24.

Joy wants to calculate mean of all the factors of 540. Help him in finding the mean of 540.

Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 540 is 1 + 2 + 3 + 4 + 5 + 6 + 9 + 10 + 12 + 15 + 18 + 20 + 27 + 30 + 36 + 45 + 54 + 60 + 90 + 108 + 135 + 180 + 270 + 540 = 1680.
Hence, the mean of factors of 540 is 1680 ÷ 24 = 70.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 540? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
Negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -90, -108, -135, -180, -270, -540.

How many factors are there for 540?

Factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
So there are in total 24 factors.

Joey wants to write all the prime factors of 540 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 540 are 2, 2, 3, 3, 3, 5.
So in exponential form it can be written as 22 x 33 x 5.

Kevin has been asked to write 23 factor(s) of 540. Can you predict the answer?

23 factor(s) of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270.