# Factors of 270

Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270

#### How to find factors of a number

 1.   Find factors of 270 using Division Method 2.   Find factors of 270 using Prime Factorization 3.   Find factors of 270 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 270

• Divide 270 by 1: 270 ÷ 1 : Remainder = 0
• Divide 270 by 2: 270 ÷ 2 : Remainder = 0
• Divide 270 by 3: 270 ÷ 3 : Remainder = 0
• Divide 270 by 5: 270 ÷ 5 : Remainder = 0
• Divide 270 by 6: 270 ÷ 6 : Remainder = 0
• Divide 270 by 9: 270 ÷ 9 : Remainder = 0
• Divide 270 by 10: 270 ÷ 10 : Remainder = 0
• Divide 270 by 15: 270 ÷ 15 : Remainder = 0
• Divide 270 by 18: 270 ÷ 18 : Remainder = 0
• Divide 270 by 27: 270 ÷ 27 : Remainder = 0
• Divide 270 by 30: 270 ÷ 30 : Remainder = 0
• Divide 270 by 45: 270 ÷ 45 : Remainder = 0
• Divide 270 by 54: 270 ÷ 54 : Remainder = 0
• Divide 270 by 90: 270 ÷ 90 : Remainder = 0
• Divide 270 by 135: 270 ÷ 135 : Remainder = 0
• Divide 270 by 270: 270 ÷ 270 : Remainder = 0

Hence, Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, and 270

#### 2. Steps to find factors of 270 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 270 using the division method, follow these steps:

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

So, the prime factorization of 270 is, 270 = 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 270 as shown below:

So, the prime factorization of 270 is, 270 = 2 x 3 x 3 x 3 x 5.

#### 3. Find factors of 270 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 270 would be the two numbers which, when multiplied, give 270 as the result.

The following table represents the calculation of factors of 270 in pairs:

Factor Pair Pair Factorization
1 and 270 1 x 270 = 270
2 and 135 2 x 135 = 270
3 and 90 3 x 90 = 270
5 and 54 5 x 54 = 270
6 and 45 6 x 45 = 270
9 and 30 9 x 30 = 270
10 and 27 10 x 27 = 270
15 and 18 15 x 18 = 270

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 270. They are called negative pair factors.

Hence, the negative pairs of 270 would be ( -1 , -270 ) , ( -2 , -135 ) , ( -3 , -90 ) , ( -5 , -54 ) , ( -6 , -45 ) , ( -9 , -30 ) , ( -10 , -27 ) and ( -15 , -18 ) .

#### 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. 270 is a factor of itself.
• 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, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270 are exact divisors of 270.
• 1 is a factor of every number. Eg. 1 is a factor of 270.
• Every number is a factor of zero (0), since 270 x 0 = 0.

• Which is the smallest prime factor of 270?

Smallest prime factor of 270 is 2.

• Is 270 a perfect square?

No 270 is not a perfect square.

• What are five multiples of 270?

First five multiples of 270 are 540, 810, 1080, 1350, 1620.

• What is prime factorization of 270?

Prime factorization of 270 is 2 x 3 x 3 x 3 x 5.

• What are factors of 270?

Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.

• How do you find factors of a negative number? ( eg. -270 )?

Factors of -270 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -90, -135, -270.

• Is 270 a whole number?

Yes 270 is a whole number.

• Which is greatest factor of 270?

The greatest factor of 270 is 135.

• What are the prime factors of 270?

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Prime factors of 270 are 2, 3, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 270. Can you help her?

Prime factors of 270 are 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 270?

Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Even factors of 270 are 2, 6, 10, 18, 30, 54, 90, 270.
Hence, product of even factors of 270 is; 2 x 6 x 10 x 18 x 30 x 54 x 90 x 270 = 85030560000.

Joy wants to calculate mean of all the factors of 270. Help him in finding the mean of 270.

Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 270 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 27 + 30 + 45 + 54 + 90 + 135 + 270 = 720.
Hence, the mean of factors of 270 is 720 ÷ 16 = 45.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 270? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -27, -30, -45, -54, -90, -135, -270.

How many factors are there for 270?

Factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
So there are in total 16 factors.

Joey wants to write all the prime factors of 270 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 270 are 2, 3, 3, 3, 5.
So in exponential form it can be written as 2 x 33 x 5.

Kevin has been asked to write 15 factor(s) of 270. Can you predict the answer?

15 factor(s) of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135.