Here we are going to discuss, what are the **factors of 7** and how many factors 7 has and what are the **factors of 7 in pairs **. Here are some methods, showing how to find the factors of 7.

*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 1 to 7, it gives 7. Here 1 and 7 are positive factors of 7 or we multiply -1 to -7, it gives 7. So -1 and -7 are negative factors of 7.

Table of Contents

## What are the Factors of 7 ?

Since factors of 7 are the numbers, which divides 7 completely without leaving remainder. So here we are

going to divide 7 by all numbers up to . 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 7 in above table are : 1, 7

Similarly, negative factors of 7 are : -1, -7

Take another example, **Factors of 9**

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

when 3 comes, because on dividing by 3, it produces the same number (3 = 3) .

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.*

## Factors of 7 in Pairs

As we saw in above table, 1 multiply by 7 gives 7. So (1, 7) or (7, 1) is a factor pair of 7.

In example of 9 ; (1, 9) or (9, 1) and (3, 3) are factor pairs.

## Methods of Prime Factors of 7

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.

**Note:** This method is not applicable for prime number.

Take example of **factors of 7 and 12**

In above example of 7

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

Any Prime Number has only one prime factor, i.e. itself.

Hence, **7 has only one prime factor i.e. 7.**

*Take another example to understand this method (Division Method).*

In second example of 12

Step 1 : First of all, we divide 12 by smallest prime number i.e. 2, it gives 6 as quotient and remainder is zero.

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

Step 2: Again we have to divide the quotient 6 by a prime number i.e. 2. It gives 3 as quotient and remainder is zero.

Step 3: Again we have to divide the quotient 3 by a prime number. Since 3 is a prime number, hence 3 will divide by itself only. So we divide 3 by 3.

Step 4. We got 1 as a quotient.

Hence, 12 = 2 x 2 x 3. So 12** has only two prime factor i.e. 2 and 3.**

### 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 7**

In factor tree method, we can initiate the tree by choosing any two factors. Here we choose 1 and 7 as factors of 7.

Since 1 is not a prime number and 7 is prime number.

Hence, 7 is prime factor of 7.

**Any Prime Number has only one prime factor, i.e. itself.**

*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.

**Factor Tree of 12**

We can initiate the tree by choosing any two factors. Here we choose 3 and 4 as factors of 12.

Further, we have to divide these nodes ( 3 & 4). Since 3 is prime number and can’t be split further. We split 4 into two factors 2 and 2.

Here we got, 2 and 3 as unique nodes. So 12 has two prime factors i.e. 2 and 3.

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

## Number of factors of 7

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

Since Method #1 is not applicable for prime number and any prime number has only two factors 1 and itself.

So 7 has only two factors 1 and 7.

To understand better, take example of 12.

12 = 2 x 2 x 3 = 2^{2} x 3 means 2 to the power 2 and 3 to the power 1

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

( Factors of 12 are 1, 2, 3, 4, 6, 12 )

if we consider both positive and negative factors, then

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

I hope, this step-by-step tutorial will be helpful to understand factorization method of 68.

Try another number 43 for factors.

Take a another look of factorization on Quora.

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