Factors Of 28 – With Division and Prime Factorization

factors of 28

Factors Of 28

Factors for 28 are numbers that divide 28 equally. They are 1,2,4,7,14, and 28. In addition, if we divide 28 by any of its factors, we will receive a natural number as the remainder. 

Suppose you divide 28 by 7, and you get 4, so 7 is a factor of 28.

28/7 = 4

Similarly, the pair factors are the number sets that result in the original number when multiplied.  Likewise, 1 multiplied by 28 is equal to 28 itself, so it is both factors of the real number 28.

1 x 28 = 28

We will use the factorization and division method to find the factors of 28.

factors of 28

What are the Factors of 28?

Factors of 28 are any natural number that divides the original number evenly without leaving a remainder.

Factors of 28:

1, 2, 4, 7, 14, and 28.

What are the Factors Of -28?

Factors of -28: –1, -2, -4, -7, -14, and -28.

In order to get the product -28, we multiply the following two numbers:

-1 x  28 =  -28

 2 x -14 =  -28

 -4 x    7  =    -28

As a result,  we have three possible pairs of factors of -28 as (-1 x  28), (2 x -14) and (-7 x 4). 

Pair Factors of 28

You can find the pair factors by multiplying the two numbers in a pair to get the original number, and the numbers are as follows:

1 × 28 = 28,   (1, 28) is a pair factor of 28.

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

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

Accordingly, the positive pair factors are (1, 28), (2, 14), and (7, 4).

Similarly, you can also find the negative pair factors of 28. Let’s follow these simple steps 

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

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

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

As a result, the negative pair factors are (-1, -28), (-2, -14), and (-7, -4).

How to Find the Factors of 28?

When finding the factors of a number, first, you need to check the factors that divide the original number completely.

For number 28, we will see what factors divide 28 equally.

  • 28 ÷ 1 = 28
  • 28 ÷ 2 = 14
  • 28 ÷ 4 = 7
  • 28 ÷ 7 = 4
  • 28 ÷ 14 = 2
  • 28 ÷ 28 = 1

Regardless of these factors, when we divide 28 by any other natural number, the result will be a fraction.

For Example:

 28 ÷ 3 = 9.33… (fraction)

Factors of 28 : 1, 2, 4, 7, 14, and 28.

Prime Factors of 28 By Division Method

As you know, 28 is a composite number, so it should have prime factors. Let’s find out how to find the prime factors.

Just follow the steps:

First divide 28 with the smallest prime factor, say 2

28 ÷ 2 = 14

Repeat the process by dividing 14 by 2.

14 ÷ 2 = 7

We get a fractional number by dividing 7 by 2, which cannot be a factor. Hence, let’s take the next prime factor, 7

7 ÷ 7 = 1

After the division process, we obtained the number 1. Therefore, we are unable to proceed. 

Consequently, the prime factors of 28 are 2 × 2 × 7 or 22 x 7, where 2 and 7 are primes.

factors of 28

Solved Examples

Q.1: If there are 28 chocolates distributed among 4 friends. How many chocolates does each friend get?

Solution:

Number of chocolates = 28

Number of friends= 4

As a result, each friend will get = 28/4 = 7 chocolates

Q.2: If there are 14 candies in one pack and the number of packs is 2, how many total candies are there in the packs?

Answer: 

There are 14 candies in each box

Total number of packs = 2

Hence, the total number of candies is 14 x 2 = 28

Q.3: How are 28 and 56 alike?

Answer: 

Factors of 28 are 1, 2, 4, 7, 14, 28 whereas factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. 

In other words, 28 and 56 have the same common factors of 1, 2, 4, 7, 8, 14, 28.

Frequently Asked Questions – FAQs

How many factors are there in 28?

Factors of 28: 1, 2, 4, 7, 14, and 28.

Is a multiple of 28 the same as a factor of 28?

Factors and multiples of 28 are not the same. Multiples of 28 are infinite, but factors of 28 are finite.

How many multiples of 28 are there?

56, 84, 112, 140, 168, 196, 224, 252, 280, 308 are the first ten multiples of 28.

Are there any prime factors in 28?

Yes, there are three primary factors in 28:  2, 2, and 7.

Do the factors 28, 32, and 48 have anything in common?

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

In the case of 32, then factors are 1, 2, 4, 8, 16, 32

There are factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Accordingly, the common factors of 28, 32, and 48 are 1, 2, and 4.

Links Related to Factors

Factors of 8=1, 2, 4, and 8.Factor of 36=1, 2, 3, 4, 6, 9, 12, 18, and 36. 
Factors of 48=1, 2, 3, 4, 6, 8, 12, 16, 24, 48Factors of 18= 1, 2, 3, 6, 9 and 18.
Factors of 24=1, 2, 3, 4, 6, 12 and 24.Factors of 25= 1, 5, and 25.
Factors of 42=  1, 2, 3, 6, 7, 14, 21, and 42.Factors of 60= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
Factors of 35= 1, 5, 7 and 35Factors of 81= 1, 3, 9, 27, 81.
Factors of 75= 1, 3, 5, 15, 25 and 75.Factors of 56=  1, 2, 4, 7, 8, 14, 28 and 56.

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