Factors of 27
Factors of 27 are numbers that, when multiplied in pairs give the product as 27. There are overall 4 factors of 27 among which 27 is the biggest factor and its positive factors are 1, 3, 9 and 27. The sum of all factors of 27 is 40. Its Prime Factors are 1, 3, 9, 27, and (1, 27) and (3, 9) are Pair Factors.
 Factors of 27: 1, 3, 9 and 27
 Negative Factors of 27: 1, 3, 9 and 27
 Prime Factors of 27: 3
 Prime Factorization of 27: 3 × 3 × 3 = 3^{3}
 Sum of Factors of 27: 40
1.  What are Factors of 27? 
2.  How to Calculate Factors of 27? 
3.  Factors of 27 by Prime Factorization 
4.  Factors of 27 in Pairs 
5.  FAQs on Factors of 27 
What are Factors of 27?
Let us recall the meaning of the term "factor." Factors of a number are the numbers that, when multiplied together, give the original number:
 Factors of a number are numbers that divide the original number completely without leaving any remainder.
 If the factors of a number are prime numbers, then the factors are said to be prime factors.
 There can be many factors of a number.
A factor is a number that divides a given number into equal parts. 3 and 9 are the factors of 27, that is, 3 divides 27 into equal parts of 9 each.
3 × 9 = 27
27 does not have 9 and 3 as its only factors. It has other factors as well. Let us see how to calculate the factors of 27.
How to Calculate the Factors of 27?
Let us learn how to calculate the factors of 27.
 Step 1: Write down the number to be factored, i.e., 27.
 Step 2: Find the two numbers whose product gives 27.
For example:
 Let's say we take 3 and 9 to be the two factors.
 3 is a prime number. Hence, it can only be factored as 1 and the number itself, i.e., 3.
 3 can be written as 3 × 1 = 3
 9 is not a prime number. Hence, it can be factorized as a product of 3 and 3, apart from the product of 1 and the number itself, i.e., 9.
 9 can be written as 3 × 3 = 9
 Thus, 27 can be written as 27= 3 × 3 × 3
Hence, the factors of 27 are 1, 3, 9, and 27. Explore factors using illustrations and interactive examples:
 Factors of 270  The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
 Factors of 23  The factors of 23 are 1, 23
 Factors of 28  The factors of 28 are 1, 2, 4, 7, 14, 28
 Factors of 12  The factors of 12 are 1, 2, 3, 4, 6, 12
 Factors of 75  The factors of 75 are 1, 3, 5, 15, 25, 75
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
Important Notes:
 Factors of any number are all the possible numbers it is divisible by. They may be prime numbers or composite numbers.
 Factors are never fractions or decimals.
 Factors can be negative.
Factors of 27 by Prime Factorization
Prime factorization is the process of writing a number as a product of its prime factors. Let us learn how to find factors using prime factorization.
 Step 1: Write the pair of factors, which on multiplication, gives the required number.
 Step 2: See the factors, whether each one of them is prime or not.
 Step 3: Follow the below criterion to differentiate between the factorization procedure.
 If both the numbers are prime, they can be multiplied as they are.
 If one among them is prime and another one is composite, then the composite number is dissociated into its factors.
 If both the numbers are composite, they can be dissociated into factors.
Factors of 27 by prime factorization are given using the following steps.
 Step 1: Write the pair of factors that, on multiplication, give the required number.
 27 can be factored as a product of 3 and 9.
 Step 2: See the factors, whether each one of them is prime or not.
 9 is not a prime number and can be dissociated as a product of 3 by 3 or as a square of 3.
 3 is a prime number, hence doesn't need any further dissociation.
 Step 3: As per the criterion, 27 can be written as 27 = 9 × 3 = 3 × 3 × 3. It can also be written as 27 = 3^{3}
Factors of 18 can be found similarly. Let's see how:
 Step 1: Write the pair of factors that, on multiplication, give the required number.
 18 can be factored as a product of 3 and 6.
 Step 2: See the factors, whether each one of them is prime or not.
 3 is a prime number, hence doesn't need any further dissociation.
 6 is not a prime number and can be dissociated as a product of 2 and 3.
Therefore, 18 can be written as 18 = 3 × 6 = 3 × 3 × 2. It can also be written as 18 = 3^{2} × 2
Challenging Questions:
 What are the factors of the following numbers using the prime factorization method?
 98
 235
 4500
Factors of 27 in Pairs
Pair factors are pairs of factors of a number that, when multiplied, give the product as the original number. Here the required number is 27. Let's try visualizing it using blocks:
Positive pair factors of 27:
Factors  Pair Factors 
1 × 27 = 27  1, 27 
3 × 9 = 27  3, 9 
9 × 3 = 27  9, 3 
27 × 1 = 27  27, 1 
Let's have a look at Negative pair factors:
Factors  Pair Factors 
1 × 27 = 27  1, 27 
3 × 9 = 27  3, 9 
9 × 3 = 27  9, 3 
27 × 1 = 27  27, 1 
Tips and Tricks:
 1 is the smallest factor of every number.
 Every number has a minimum of two factors, i.e., 1 and the number itself.
 All even numbers always have 2 as one of their factors.
 All the numbers which end in 5 will always have 5 as one of their factors.
 All the numbers which end in 0 will always have 1, 2, 5, and 10 as their factors.
Factors of 27 Solved Examples

Example 1: Three friends plucked 27 mangoes from a tree and distributed them among themselves equally. How many would each one of them get?
Solution:
27 mangoes are to be divided among 3 friends equally. This implies we need to divide 27 by 3.
27/3 = 9
Hence, each child will get 9 mangoes.

Example 2: Help John find the positive pairs of factors of 36.
Solution:
Positive pair factors of 36 are given as:
Factors Pair Factors 1 × 36 = 36 1, 36 2 × 18 = 36 2, 18 3 × 12 = 36 3, 12 4 × 9 = 36 4, 9 6 × 6 = 36 6, 6 9 × 4 = 36 9, 4 12 × 3 = 36 12, 3 18 × 2 = 36 18, 2 36 × 1 = 36 36, 1 Hence, John has found the positive pairs of factors of 36.

Example 3: Which number on multiplying with 6 gives 48?
Solution:
The negative factor pairs of 48 are:
(1, 48), (2, 24),(3, 16),(4, 12), (6, 8)
Therefore when 8 is multiplied by 6, the product is 48 i.e. 6 × 8 = 48.

Example 4: Anna has 54 units of a cutlery set. She wants to pack it in cartons such that these units are evenly distributed. There are two sizes of cartons available to her. One size has a capacity of 9 units and the other size has a capacity of 12 units. Which size of the carton will she choose so that there is no unit left and maximum units are filled in the cartons?
Solution:
The units must be evenly distributed and no units should be left behind. This implies the number of units in each carton must be a factor of 54.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
12 is not a factor of 54 whereas 9 is a factor of 54. Hence, Anna will choose the carton with a capacity of 9 units.

Example 5: A rectangle has an area of 40 square inches and a length of 10 inches. Determine its breadth.
Solution:
The area of the rectangle is length × breadth. The length of the rectangle, i.e., 10 inches, is a factor of the area, i.e., 40 square inches.
When 4 is multiplied by 10, the product is 40 i.e. 4 × 10 = 40
Therefore, the breadth of the rectangle is 4 inches.
FAQs on Factors of 27
What are the Factors of 27?
The factors of 27 are 1, 3, 9, 27 and its negative factors are 1, 3, 9, 27.
What is the Greatest Common Factor of 27 and 4?
The factors of 27 are 1, 3, 9, 27 and the factors of 4 are 1, 2, 4. 27 and 4 have only one common factor which is 1. This implies that 27 and 4 are coprime.
Hence, the Greatest Common Factor (GCF) of 27 and 4 is 1.
What are the Prime Factors of 27?
The prime factor of 27 is 3.
How Many Factors of 27 are also Factors of 20?
Since, the factors of 27 are 1, 3, 9, 27 and factors of 20 are 1, 2, 4, 5, 10, 20. Hence, 27 and 20 have only one common factor which is 1. Therefore, 27 and 20 are coprime.
What is the Sum of the Factors of 27?
All the Factors of 27 are 1, 3, 9, 27 and therefore the sum of all these factors is 1 + 3 + 9 + 27 = 40
visual curriculum