# Factors of 27

Factors of 27 are 1, 3, 9, and 27

#### How to find factors of a number

 1.   Find factors of 27 using Division Method 2.   Find factors of 27 using Prime Factorization 3.   Find factors of 27 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 27

• Divide 27 by 1: 27 ÷ 1 : Remainder = 0
• Divide 27 by 3: 27 ÷ 3 : Remainder = 0
• Divide 27 by 9: 27 ÷ 9 : Remainder = 0
• Divide 27 by 27: 27 ÷ 27 : Remainder = 0

Hence, Factors of 27 are 1, 3, 9, and 27

#### 2. Steps to find factors of 27 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 27 using the division method, follow these steps:

• Step 1. Start dividing 27 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 27, which is 3. Divide 27 by 3 to obtain the quotient (9).
27 ÷ 3 = 9
• Step 3. Repeat step 1 with the obtained quotient (9).
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 27 is, 27 = 3 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 27 as shown below:

So, the prime factorization of 27 is, 27 = 3 x 3 x 3.

#### 3. Find factors of 27 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 27 would be the two numbers which, when multiplied, give 27 as the result.

The following table represents the calculation of factors of 27 in pairs:

Factor Pair Pair Factorization
1 and 27 1 x 27 = 27
3 and 9 3 x 9 = 27

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 27. They are called negative pair factors.

Hence, the negative pairs of 27 would be ( -1 , -27 ) , ( -3 , -9 ) .

#### How do you explain factors?

In mathematics, a factor is a number or also it can be an algebraic expression that divides another number or any expression completely and that too without leaving any remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Every number is a factor of zero (0), since 27 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, 3, 9, 27 are exact divisors of 27.
• Factors of 27 are 1, 3, 9, 27. Each factor divides 27 without leaving a remainder.

• Which is the smallest prime factor of 27?

Smallest prime factor of 27 is 3.

• Is 27 a perfect square?

No 27 is not a perfect square.

• What are five multiples of 27?

First five multiples of 27 are 54, 81, 108, 135, 162.

• What is prime factorization of 27?

Prime factorization of 27 is 3 x 3 x 3.

• What are factors of 27?

Factors of 27 are 1, 3, 9, 27.

• How do you find factors of a negative number? ( eg. -27 )?

Factors of -27 are -1, -3, -9, -27.

• Is 27 a whole number?

Yes 27 is a whole number.

• Which is greatest factor of 27?

The greatest factor of 27 is 9.

• What are the prime factors of 27?

The factors of 27 are 1, 3, 9, 27.
Prime factors of 27 are 3, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 27. Can you help her?

Prime factors of 27 are 3, 3, 3.
Hence, the product of prime factors of 3.

Can you help Rubel to find out the product of the even factors of 27?

Factors of 27 are 1, 3, 9, 27.
Even factors of 27 are 0.
Hence, product of even factors of 27 is; 0 = 0.

Joy wants to calculate mean of all the factors of 27. Help him in finding the mean of 27.

Factors of 27 are 1, 3, 9, 27.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 27 is 1 + 3 + 9 + 27 = 40.
Hence, the mean of factors of 27 is 40 ÷ 4 = 10.00.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 27? Help her in writing all the factors.

Positive factors are 1, 3, 9, 27.
Negative factors are -1, -3, -9, -27.

How many factors are there for 27?

Factors of 27 are 1, 3, 9, 27.
So there are in total 4 factors.

Joey wants to write all the prime factors of 27 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 27 are 3, 3, 3.
So in exponential form it can be written as 33.

Kevin has been asked to write 3 factor(s) of 27. Can you predict the answer?

3 factor(s) of 27 are 1, 3, 9.