Here we are going to discuss, what are the **factors of 28** and how many factors 28 has and what are the **factors of 28 in pairs **. Here are some methods, showing how to find the factors of 28.

*Actually, Factor is a number which divides any number completely without leaving remainder.*

*Or simply we can say that if we multiply two whole numbers (positive & negative) and it gives a product. Then **the numbers that we multiply, are the factors of the product.*

For example, if we multiply 4 to 7, it gives 28. Here 4 and 7 are positive factors of 28 or we multiply -2 to -14, it gives 28. So -2 and -14 are negative factors of 28.

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## What are the Factors of 28 ?

Since factors of 28 are the numbers, which divides 28 completely without leaving remainder. So here we are

going to divide 28 by all numbers up to 28. Let’s see the process –

We have to stop the process, if any number of column ‘B’ appears in column ‘A’.

Here we stop the division when 7 appears in column ‘A’, which has already been came in column ‘B’.

Hence, positive factors of 28 in above table are : 1, 2, 4, 7, 14, 28

Similarly, negative factors of 28 are : -1, -2, -4, -7, -14, -28

Take another example, **Factors of 25**

In above example, no element of Column ‘B’ appears in Column ‘A’, but we stopped the process

when 5 comes, because on dividing by 5, it produces the same number (5 = 5) .

So we have to stop the process when any element comes in both columns at same level.

And this element will consider as a factor.

*Note :- This situation occurs with a perfect square number, such as 9, 16, 25, 36, 49 etc.*

## Factor pairs of 28

As we saw in above table, 1 multiply by 28 gives 28. So (1, 28) or (28, 1) is a factor pair of 28.

Similarly, (2, 14) and (4, 7) are another factor pairs of 28.

In example of 25 ; (1, 25) or (25, 1) and (5, 5) are factor pairs.

## Methods of Prime Factors of 28

Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.

### Method #1 (Division Method)

**Step 1 :** Divide the number by the smallest prime number, which divides the number exactly.

**Step 2 :** Divide the quotient again by the smallest prime number. If quotient is not exactly divisible by the

smallest prime number, choose next smallest prime number.

**Step 3 :** Repeat Step 2 again and again till the quotient becomes 1.

**Step 4 :** All the prime numbers used in above process are the prime factors.

Check : Multiply all the prime factors, the multiplication should be the number itself.

Caution : In this method, only prime numbers will be use to divide.

Take example of 28 and 35

In above example of 28

Step 1 : First of all, we divide 28 by smallest prime number i.e. 2, it divide 28 completely and gives 14 as quotient.

(Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)

Step 2: Again we divide 14 by prime number i.e. 2, it gives 7 as quotient.

Step 3: Since 7 is a prime number, hence it will divide by itself only.

Hence, 28 = 2 x 2 x 7. So** 28 has two prime factor i.e. 2 and 7.**

In second example of 35

Step 1 : First of all, we divide 35 by smallest prime number i.e. 2, but it doesn’t divide completely. So try next prime numbers 3 and 5. On dividing by 5, we get 7 as quotient.

(Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)

Step 2: Since 7 is a prime number, hence it will divide by itself only.

Hence, 35 = 5 x 7 = 5 x 7

So 35 has two prime factor i.e. 5 & 7.

### Method #2 (Factor Tree Method)

**Step 1 :** Write a number as root of the tree

**Step 2 :** Find the factors of the number, each factor will be considered as root again (now, we got 2 new root)

**Step 3 :** Repeat step 2 until we can’t factor any more (or until we got prime factor)

**Step 4 :** The end nodes are the prime factors.

**Factor Tree of 28**

In factor tree method, we can initiate the tree by choosing any two factors. Here we choose 2 and 14 as factors of 28.

Further, we divide 14 in two factors, i.e. 7 and 2. Since both are prime numbers and can not be further split.

Hence, we got 2, 2, 7 are nodes, in which 2 and 7 are unique nodes.

*Note:- The Factor Tree may be made so many types depends upon choosing the initial and middle factors.*

In factor tree, all nodes and unique nodes will be same, it doesn’t depend tree. We can choose any initial nodes and middle nodes.

## Number of factors of 28

To find the number of factors, we use **Method #1 (Division Method).**

In our example, as we saw above 28 = 2 x 2 x 7 = 2^{2} x 7 means 2 to the power 2 multiply 7 to the power 1

** Number of factors is = (power + 1)(power + 1)(power + 1)……….** = (2 + 1)(1 + 1) = 3 x 2 = 6

if we consider both positive and negative factors, then

total no. of factors = 6 (positive) + 6 (negative) = 12

Take another example, 35 = 5 x 7 = 5^{1} x 7^{1}

Number of factors of 35 is = (1 + 1)(1 + 1) = 2 x 2 = 4

and if we consider both positive and negative factors, then

total no. of factors = 4 (positive) + 4 (negative) = 8

I hope, this step-by-step tutorial will be helpful to understand factorization method of 28.

Try another number 99 for factors.

Take a another look of factorization on Quora.

[…] another number 28 for […]