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Factors of 28
Factors of 28 are the list of integers that we can split evenly into 28. There are 6 factors of 28 of which 28 itself is the biggest factor and its positive factors are 1, 2, 4, 7, 14 and 28. The sum of all factors of 28 is 56. Its Prime Factors are 1, 2, 4, 7, 14, 28 and (1, 28), (2, 14) and (4, 7) are Pair Factors.
 Factors of 28: 1, 2, 4, 7, 14 and 28
 Negative Factors of 28: 1, 2, 4, 7, 14 and 28
 Prime Factors of 28: 2, 7
 Prime Factorization of 28: 2 × 2 × 7 = 2^{2} × 7
 Sum of Factors of 28: 56
1.  What Are the Factors of 28? 
2.  How to Calculate the Factors of 28? 
3.  Factors of 28 by Prime Factorization 
4.  Factors of 28 in Pairs 
5.  FAQs on Factors of 28 
What are Factors of 28?
The factor of a number is that number that divides it completely without leaving any remainder. The number 28 is an even composite number i.e it is divisible by 2. The factors of 28 are pairs of those numbers whose product gives the value 28.
How to Calculate Factors of 28?
 Step 1: Write down the number to be factored, i.e. 28
 Step 2: Find the two numbers whose product gives 28
 Let's say we take 2 and 14 as the numbers.
 2 is a prime number. Hence, it can only be factored as 1 and the number itself, i.e. 2
 2 can be written as 2 = 2 × 1
 14 is not a prime number. Hence, it can be factored as 2 and 7, apart from 1 and the number itself, i.e. 14
 14 can be written as 14 = 7 × 2 × 1
Hence, 28 can be factored as 28 = 7 × 2 × 2 × 1 which means that the Factors of 28 are 1, 2, 4, 7, 14, and 28
Important Notes:
 Factors of any number include all the possible numbers it is divisible by. They may be prime numbers or composite numbers. In this case, 28 is a composite number but 2 is a prime number.
 Factors are always whole numbers. They are never fractions or decimals. For example, even though the product of 56 and 0.5 is 28, they cannot be considered as factors of 28.
Explore factors using illustrations and interactive examples
 Factors of 36  The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
 Factors of 24  The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
 Factors of 32  The factors of 32 are 1, 2, 4, 8, 16, 32
 Factors of 128  The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128.
 Factors of 120  The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
 Factors of 288  The factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
Factors of 28 by Prime Factorization
Writing a number as a product with all its factors being prime is called prime factorization. Let's learn how to find factors using prime factorization.
 Step 1: Write the pair of factors that on multiplication gives the required number.
 Step 2: Check the factors to see if 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 it is.
 If one among them is prime and the other 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 28 by prime factorization are given by using the following steps.
 Step 1: 28 can be factored as the product of 4 and 7.
 Step 2: 4 is not a prime number and can be dissociated as a product of 2 by itself or as a square of 2. 7 is a prime number. Hence, it doesn't need any further dissociation.
 Step 3: 28 can thereby be written as 28 = 4 × 7 = 2 × 2 × 7. The prime factors of 28 can also be written as 28 = 2^{2} × 7. Now that we have done the prime factorization of our number, we can multiply them and get the other factors. Can you try and find out if all the factors are covered or not?
Factors of 28 in Pairs
Pair factors are pairs of those numbers which when multiplied give the required number as the product. Here, the required number is 28. Let's try visualizing it using blocks.
Positive pair factors of 28:
Factors  Pair factors 

1 × 28 = 28  (1, 28) 
2 × 14 = 28  (2, 14) 
4 × 7 = 28  (4, 7) 
7 × 4 = 28  (7, 4) 
14 × 2 = 28  (14, 2) 
28 × 1 = 28  (28, 1) 
Negative pair factors of 28:
Factors  Pair factors 

1 × 28 = 28  (1,  28) 
 2 × 14 = 28  ( 2,  14) 
 4 × 7 = 28  ( 4,  7) 
7 × 4 = 28  ( 7,  4) 
14 × 2 = 28  ( 14,  2) 
28 × 1 = 28  ( 28,  1) 
Tips and Tricks:
 1 is the smallest factor of every number.
 28 is an even number. Hence, 2 is one of its factors.
Factors of 28 Solved Examples

Example 1: Seth wanted to count all the positive and negative factors of 28. Help him count them.
Solution:
The positive factors of 28 are 1, 2, 4, 7, 14, and 28. The negative factors of 28 are 1, 2, 4, 7, 14, and 28.
Therefore, Seth found 12 factors in total.

Example 2: Aubrey had to distribute 28 food packets among 16 children. Find the extra number of packets she will require if they can't be distributed equally.
Solution:
To show the distribution of 28 food packets among 16 children mathematically, we say 28 ÷ 16 which means that 28 is not entirely divisible by 16. The closest number to 28 completely divisible by 16 is 32.
Hence, Aubrey will require 4 more packets.

Example 3: Help Augustus find the pair factors of 28 which on addition gives 16, subtraction gives 12, and division gives one of the factors of 28 which belongs to another pair.
Solution:
Addition of pair factors = 16, subtraction of pair factors = 12. Division of pair factors = One factor belonging to another pair
The pair factor is (14, 2). The pair factors on addition give 16, subtraction gives 12, and division gives 7 which is another factor of 28 and is a part of another pair factor. Therefore, Augustus found (14, 2) is the pair factor.

Example 4: Determine whether 28 is a perfect number or not?
Solution:
The numbers whose factors excluding the number itself add up resulting in the same number are called perfect numbers. Factors of 28 are 1, 2, 4, 7, 14, and 28.The addition of factors of 28 excluding 28 gives: 1 + 2 + 4 + 7 + 14 = 28.
As the sum of the factors of 28 (excluding 28) results in 28, it is a perfect number. Thus, 28 is a perfect number.
FAQs on Factors of 28
What are the Factors of 28?
The factors of 28 are 1, 2, 4, 7, 14, 28 and its negative factors are 1, 2, 4, 7, 14, 28.
What Numbers are the Prime Factors of 28?
The prime factors of 28 are 2, 7.
What is the Greatest Common Factor of 28 and 26?
The factors of 28 and 26 are 1, 2, 4, 7, 14, 28 and 1, 2, 13, 26 respectively.
Common factors of 28 and 26 are [1, 2].
Hence, the GCF of 28 and 26 is 2.
What are the Common Factors of 28 and 11?
Since the factors of 28 are 1, 2, 4, 7, 14, 28, and factors of 11 are 1, 11. Hence, 28 and 11 have only one common factor which is 1. Therefore, 28 and 11 are coprime.
What is the Sum of the Factors of 28?
Factors of 28 are 1, 2, 4, 7, 14, 28 and, the sum of all these factors is 1 + 2 + 4 + 7 + 14 + 28 = 56
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