Factors

# Factors of 27 | Prime Factorization of 27 | Factor Tree of 27

Written by Prerit Jain

Updated on: 08 Jun 2023

Contents

### Factors of 27 | Prime Factorization of 27 | Factor Tree of 27

## Factors of 27

Factors of 27 | Factor Pairs of 27 | Prime factors of 27 |

1, 3, 9, 27 | (1,27) (3,9) (9,3) | 3 x 3 x 3 |

**Factors of 2**7,

**Factor Pairs of 2**7,

**Prime factors of 2**7

Calculate Factors of

**The Factors are**

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## What are the factors of 27

The factors of a number are the numbers that divide into the given number evenly (without a remainder). There are several methods you can use to find the factors of a number, such as listing, factor pairs, prime factorization, and division.

To find the factors of 27 using the listing method, you can make a list of the numbers from 1 to 27 and check which ones divide into 27 evenly. The factors of 27 are 1, 3, 9, and 27.

To find the factors of 27 using the factor pairs method, you can list the pairs of numbers that multiply together to equal 27. The factor pairs of 27 are (1, 27), (3, 9), and (-1, -27).

To find the factors of 27 using prime factorization, you can start by dividing 27 by the smallest prime number that divides it evenly (in this case, 3). This process can be repeated until you are left with only prime numbers. The prime factorization of 27 is 3 x 3 x 3, which means that the factors of 27 are 1, 3, 9, and 27.

To find the factors of 27 using the division method, you can start by dividing 27 by the smallest possible number (usually 2) and see if the result is a whole number. If it is, then the result is a factor of 27. You can then divide the result by the next smallest possible number and repeat the process until you reach a number that is not a whole number. The factors of 27 that we can find using the division method are 1, 3, and 9.

## How to Find Factors of 27

Here are four methods to find the factors of 27:

- Factors of 27 using the Multiplication Method
- Factors of 27 using the Division Method
- Prime Factorization of 27
- Factor tree of 27

## Factors of 27 Using the Multiplication Method

- Start with the number 27.
- Divide 27 by the smallest possible number, which is 2. If the result is a whole number, then 2 is a factor of 27. In this case, the result is 13.5, which is not a whole number, so 2 is not a factor of 27.
- Divide 27 by the next smallest number, which is 3. If the result is a whole number, then 3 is a factor of 27. In this case, the result is 9, which is a whole number, so 3 is a factor of 27.
- Continue dividing 27 by numbers until you reach the square root of 27, which is approximately 5.196.
- The factors of 27 are 1, 3, and 9.

To check your work, you can multiply these factors together to see if you get 27. If the product is equal to 27, then you have correctly identified the factors of 27.

## Factors of 27 Using the Division Method

- Begin by writing down the number 27.
- Start dividing 27 by the smallest possible number, which is 1. If the result is a whole number, then 1 is a factor of 27. In this case, the result is 27, which is a whole number, so 1 is a factor of 27.
- Continue dividing 27 by numbers until you reach the square root of 27, which is approximately 5.196.
- The factors of 27 are 1, 3, and 9.

To confirm your results, you can divide 27 by each of the factors to see if the result is a whole number. If it is, then the factor is a valid factor of 27.

Alternatively, you can also find the factors of 27 by starting with the number 27 and dividing it by the largest possible number, which is 27. The result is 1, so 27 is a factor of 27. You can then continue dividing 27 by numbers in decreasing order until you reach the square root of 27. This will give you the same set of factors as the previous method.

## Prime Factorization of 27

Calculate Prime Factors of

The Prime Factors of 27 =

3 x

3 x

3

The prime factorization of 27 is the expression of 27 as the product of its prime factors. The prime factorization of 27 is 3 x 3 x 3 because 27 can be expressed as the product of three 3s (3 x 3 x 3 = 27).

To find the prime factorization of a number, you can express the number as the product of its prime factors. For example, the prime factorization of 24 is 2 x 2 x 2 x 3, because 24 can be expressed as the product of the prime numbers 2, 2, 2, and 3 (2 x 2 x 2 x 3 = 24).

The prime factorization of a number is written as the product of its prime factors. For example, the prime factorization of 27 is written as 3 x 3 x 3.

## Factor tree of 27

A factor tree is a graphical representation of the prime factorization of a number. It is a way to find the prime factors of a number by breaking it down into smaller and smaller numbers until we are left with only prime numbers. To create a factor tree, we start by writing the number at the top of the tree and then dividing it by the smallest possible prime number that divides it evenly. The result becomes the first branch of the tree. We continue dividing each branch by the smallest possible prime number until we are left with only prime numbers. The prime factorization of 27 is 2 x 11, which means that the prime factors of 27 are 2 and 11.

## Factor Pairs of 27

Calculate Pair Factors of

1 x 27=27

3 x 9=27

9 x 3=27

So Pair Factors of 27 are

(1,27)

(3,9)

(9,3)

The factor pairs of 27 are the pairs of numbers that can be multiplied together to equal 27. These pairs include (1, 27), (3, 9), (9, 3), and (27, 1).

To find the factor pairs of 27, you can use either the multiplication or division method. The multiplication method involves starting with the number 1 and multiplying it by 27 to get the first factor pair, then continuing to multiply by other numbers until you reach the square root of 27. The division method involves starting with the number 27 and dividing it by the smallest possible number, then continuing to divide by other numbers until you reach the square root of 27.

The factors of 27 are 1, 3, and 9, and these numbers can be arranged in different pairs to create the factor pairs of 27. For example, the pair (1, 27) consists of factors 1 and 27, and the pair (3, 9) consists of factors 3 and 9.

## Factors of 27 – Quick Recap

**Factors of 27:**1, 3, 9, and 27.**Negative Factors of 27:**(-1, -27) and (-3, -9).**Prime Factors of 27:**3 x 3 x 3**Prime Factorization of 27:**3 x 3 x 3

## Factors of 27 – Fun Facts

1. 27 is a composite number, meaning it has more than two factors.

2. The prime factors of 27 are 3 and 9; 3 x 9 = 27.

3. All multiples of 3 and 9, up to 81, are also factors of 27.

4. At least three consecutive odd numbers need to be multiplied together to create a product that is divisible by 27 (i.e., 3 x 5 x 7 = 105).

5. The sum of all the positive divisors of 27 (excluding itself) is 36, making it a perfect number.

6. There are 8 distinct pairings that can be used to multiply together in order to generate one hundred eleven (i.e., 11×11=111 & 3×37= 111).

7. The greatest common factor (GCF) between any two or more numbers is always less than or equal to the smallest number among them (i.e., for 27 and 36, the GCF is 9).

8. 27 is a perfect cube because it can be expressed as the cube of an integer. It is equal to 3 x 3 x 3, or 3^3.

**Also Check**: Multiples, Square Root, and LCM

Solved Example of Factor of 27

**Q.1:List all the pairs of factors for 27 in increasing order. Solution: **The pairs of factors for 27 in increasing order are (1,27), (3, 9), and (9, 3).

**Q.1:What is the smallest number that can go into 27? Solution: **The smallest number that can go into 27 is 1 since any number divided by 1 will remain unchanged.

**Q.2:Is there any perfect square within the range of numerators from 25 to 29? Solution: **Yes, there is one perfect square within this range; 29² = 84.

**Q.3:Does 28 have any cube factors? If so name them… Solution:** Yes, 28 has two cube factors; 2³ = 8 and 7³ = 343.

**Q.4:Find two numbers that multiply together to equal 27. Solution:** The two numbers that multiply together to equal 27 are 3 and 9 , since 3 x 9 = 27.

**Q.5:How many even factors does 27 have? Solution:** There are two even factors of 27; 2 and 6.

**Q.6:Explain why 183568576704081 can be written as a product of three primes. Solution:**183568576704081 can be written as a product of three primes because it can be factored into its prime components as follows – 183568576704081 = 13 × 13 × 17959117.

** Q.7:What would be the least common multiple between 21 and 24? Solution: **The least common multiple between 21 and 24 is 504.

**Q.8:Find the prime factorization of 27. Solution: **The prime factorization of 27 is 3 x 3 x 3; since 3 x 3 x 3 =27.

**Q.9:What is the greatest common factor for 22 and 26? **** Solution: **The greatest common factor for 22 and 26 is 2 since 2 is the only integer between them which can be evenly divided into both numbers without a remainder (no shared divisors).

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## Frequently Asked Questions on Factors of 27

**What is the greatest common factor (GCF) of 27?**

The greatest common factor (GCF) of 27 is 3; it’s the largest number and both can be divided without a remainder.

**How many factors does twenty-seven have?**

Twenty-seven has six different factors; these include 1, 3, 9, and

27.

**Is 18 a multiple or a factor of 27?**

18 is a multiple but not a factor of twenty-seven as it cannot be divided evenly with no remainder (18/27 =0.6666666667).

**Find three prime numbers whose product equals eighty-one when multiplied together.**

Three prime numbers whose product equals eighty-one when multiplied together are 3, 3, and 9;3x3x9= 81.

**Henry needs to divide an equation into equal parts however each part must be divisible by nine; what equation could he use?**

Henry could use 54×3=162 as this equation can be divided into two equal parts both divisible by nine (162/9 =18 & 162/18 = 9).

**How many odd numbers remain between 1-27 when all even numbers are removed?**

Thirteen odd numbers remain between one and twenty-seven when all even numbers are removed; these would include 1, 3, 5, 7, 9, 11, 13, 15, 17 19, 21, 23 & 25.

**Find two prime numbers that can only be divided evenly by themselves and one to generate a product that totals eighty-four.**

Two prime numbers that can only be divided evenly by themselves and one to generate a product that totals eighty-four are 84 & 1;84×1=84and neither can be divided evenly with another number apart from themselves or one in order to equal eighty-four.

**If there are five unequal numbers multiplied together which is the greatest possible total if their product equals ninety?**

The greatest possible total if five unequal numbers multiplied together equal ninety is 18;1x2x3x6x18=90

**How many pairs of factors are needed in order to multiply together in order to generate one hundred eleven?**

Two pairs of factors need multiplying together in order to generate one hundred eleven; these would include 11×11=111 & 3 x37= 111.

**What two consecutive odd numbers add up to thirty while their product remains divisible by nine?**

Two consecutive odd numbers adding up to thirty while keeping their product divisible by nine are 13& 15(13+15 = 30 & 13×15 =195);195/9 = 2.

Written by

Prerit Jain