Factors Of 28 | With Easy Division and Prime Factorization

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.

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 (-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.

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, and 28.

Example 1:

What are the common factors between 28 and 24?

Solution:

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

1, 2, 3, 4, 6, 8, 12, and 24 are the factors of 24.

Hence, 28 and 24 have common factors of 1, 2, and 4.

Example 2:

Calculate the common factors of 62 and 6.

Solution:

Factors of 62: 1, 2, 31, and 62.

Factors of 6=1, 2, 3, and 6

Hence, 62 and 6 have common factors of 1 and 2.

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