Factors of 28

The factors of 28 are those two numbers multiplied together to get a result of 28. These two numbers are called factor pairs. Factor pairs of the number 28 are whole numbers. They can be either positive or negative but never fraction or decimal numbers. 


In this article, we will discuss the ways to find all factors of 28.


The Factorization Method

The factorization method involves reducing a number down to its smaller, simpler parts or factors. It requires the understanding of division, real numbers, and rational numbers. Using this we can find what are the factors of 28.


The first step in the factorization method is to take the numbers 1 and 28 as factors of 28. Then find the other pair of numbers which give the original number, 28.


We will show the factorization method as well as the method of prime factorization of 28.


The factors of 28 are 1, 2, 4, 7, 14, 28.


What are the Factors of 28?

The Factor Pairs of 28

The Prime Factorisation of 28

(1,28), (2,14), (4,7)

2 x 2 x 7


What are the Factor Pairs of 28?

To find the factor pairs, multiply the two numbers to get 28.  


1 × 28 = 28, making (1, 28) the first pair factor of 28.


Next, 2 × 14 = 28, so (2, 14) is a pair factor of 28; and 


4 × 7 = 28, making (4, 7) another pair factor of 28.


This is true for the converse as well,


28 × 1 = 28; (28, 1) is a pair factor


14 × 2 = 28; (14, 2) is a pair factor and


7 × 4 = 28; (7, 4) is also a pair factor of 28.


Note that converse factor pairs of 28 are the same. In other words, pair factor (1, 28) is the same as (28, 1), (2, 14) as (14, 2), and (7, 4) as (4, 7).


There are only 3positive pair factors-(1, 28), (2, 14), and (7, 4).

As mentioned above, we have to consider the negative pair factors as well. Proceed with the following steps to find them. 


-1 × -28 = 28; (-1, -28) is a pair factor, 


-2 × -14 = 28; (-2, -14) is a pair and


-4 × -7 = 28, (-4, -7) is a pair factor.


As multiplication works,


-28 × -1 = 28, so (-28, -1) is also a pair factor. Similarly,


-14 × -2 = 28; (-14, -2) is a pair factor and


-7 × -4 = 28; (-7, -4) is also a pair factor.


So the negative pair factors are (-1, -28), (-2, -14), and (-7, -4). These are included as the common factors of 28. 


What are the Factors of 28: Steps to Calculate: 

These are the following steps to calculate the factors of a number 28

  1. Write the number 28 down. 

  2. Deduce two or more numbers, giving the result of 28 after multiplication. For example, 2 and 14.

  3. Now, 2 is a prime number that contains only two factors. A prime number has only two factors- 1 and the number itself( 1 and 2). So that it cannot be further factorized.
    Number 14 is a composite number. This means it can be further factored.

14 can be written as 2 x 7 x 1

Therefore, the prime factorization of 28 is written as 28 = 2 × 2 × 7.

  1. Finally, write down all the unique numbers which we can obtain from 2 × 2 × 7 x 1.


Prime Factorization of 28 By Division Method

The next question that might come to mind is what is the prime factorization of 28 exactly?


The number 28 is a composite number having prime factors. In order to find them, the division method is used. Here is how you find the prime factorization of 28.


The first step in the division method is to divide the number 28 with the smallest prime factor, 2.


28 ÷ 2 = 14


Next divide 14 by 2.


14 ÷ 2 = 7


Now, we know that 7 is not divisible by 2. A result is a fractional number, which cannot be a factor. So, you divide 7 with the next divisible prime number, 7,


7 ÷ 7 = 1


Once we get the number 1 the division process ends. We cannot proceed further. When you write the prime factorization of 28, it will be written as 2 × 2 × 7 or 22 x 7, where 2 and 7 are the prime numbers.


Finding the factors of 28 is easy when you know how to find them. These methods aren’t restricted to just the number 28; they can be used for other numbers as well!

FAQ (Frequently Asked Questions)

1. What are all Factors of 28?

Answer: The number 28 can be written as 1 x 2 x 2 x 7. All the factors of 28 can be found out through the methods of factorization and division. Through the factorization, the factors of 28 are found to be 1, 2, 4, 7, 14, and 28. The pair factors are (1,28), (2,14), (4,7), (-1,-28), (-2,-14), (-4,-7).


Taking it a step further involves prime factorization using the division method. When dividing the composite number 28 into prime factors, we find the factors to be 2 × 2 × 7 or 22 x 7.

2. What are all the Factors for 28 and How do They Differ From the Multiples of 28?

Answer: There is a clear distinction between the factors and multiples of 28. A factor is a number dividing a specific number completely without a remainder. Taking the case of 28, all of its factors i.e. 1, 2, 4, 7, 14, and 28 can divide 28 to give a whole number. Factors are finite.


Multiples on the other hand are infinite. They are the results of multiplying a specific number with another number. For example, 28 x 1= 28, 28 x 2= 56, 28 x 3= 84, 28 x 4=112 and so one. 28, 56, 84 are all multiples of 28.