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 that 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

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

The Prime Factorisation of 28
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
Write the number 28 down.
Deduce two or more numbers, giving the result of 28 after multiplication. For example, 2 and 14.

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.

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!

Quick tips

• 1 is the smallest and a common factor of every number.

• Every even number is always divisible by 2. Hence, 2 is one of the factors of 28.

Let us look at some examples to grasp the concept of factorization of 28 better.

1. There are 28 pieces of a cake which are to be distributed among 7 kids. How many pieces of cake will each kid get?

Solution: 

Total number of pieces of the cake: 28

Total number of kids: 7

Now in order to calculate the number of pieces each kid will get, we will use the Prime Factorization of 28 by Division Method for which the divisor is 7. Therefore, 28÷7 = 4. So, each kid will get 4 pieces of cake.

2. If Sandra has 28 chocolates and she wants to give to 16 children, how many more chocolates will she need to distribute equally?

Solution: Like in example 1, to get the number of chocolates to be distributed equally among 16 children, we have to use the division method on 28, that is, 28÷16 but 28 is not totally divisible by 16 and leaves a remainder of 12 when the quotient is 1, therefore, we can say that the additional number of chocolates Sandra needs to distribute equally is 4, and 28+4 equals to 32 which when divided by 16 gives 2. Therefore, each child will get 2 chocolates. 

3. What are the common factors of 58 and 28?

Solution: The factors of 28 are 1,2,4,7,14,28 which can be written as 2×2×7×1 and the factors of 58 are 1,2,29,58 which can be written as 2×29×1. So, the common factors are 1 and 2, that is, 2×1.

4. If there are 14 pairs of shoes in a shoe closet, what is the total number of shoes in the shoe closet?

Solution: A pair consists of 2 units of things taken together. Given,

number of pairs of shoes: 14

Therefore, there are a total of 14×2 = 28 numbers of shoes in the shoe closet.

5. Which is/are the pair factor or factors of 28 which satisfies all the conditions on:

(i) addition gives 16,

(ii) subtraction gives 12, and

(iii) division gives another factor of 28?

Solution: The factors of 28 are 1,2,4,7,14 and 28 out of which only the pair factor (2,14) satisfies all the conditions. On adding, 14+2=16, on subtraction 14-2 gives 12 and on dividing 14 by 2, the answer is 7 which is one of the factors of 28. Hence, the answer is (2,14).