Here we are going to discuss, what are the **factors of 39** and how many factors 39 has and what are the **factors of 39 in pairs **. Here are some methods, showing how to find the factors of 39.

*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 3 to 13, it gives 39. Here 3 and 13 are positive factors of 39 or we multiply -1 to -39, it gives 39. So -1 and -39 are negative factors of 39.

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## What are the Factors of 39 ?

Since factors of 39 are the numbers, which divides 39 completely without leaving remainder. So here we are

going to divide 39 by all numbers up to 39. 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 13 appears in column ‘A’, which has already been came in column ‘B’.

Hence, positive factors of 39 in above table are : 1, 3, 13, 39

Similarly, negative factors of 39 are : -1, -3 -13, -39

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 39

As we saw in above table, 1 multiply by 39 gives 39. So (1, 39) or (39, 1) is a factor pair of 39.

Similarly, (3, 13) is another factor pairs of 39.

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

## Methods of Prime Factors of 39

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 **factors of 39 and 52**

In above example of 39

Step 1 : First of all, we divide 39 by smallest prime number i.e. 2. But it doesn’t divides completely. So try next prime number i.e. 3. It gives 13 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: Since 13 is a prime number, hence it will divide by itself only.

Hence, 39 = 3 x 13. So** 39 has two prime factor i.e. 3 and 13.**

In second example of 52

Step 1 : First of all, we divide 52 by smallest prime number i.e. 2, it gives 26 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 26 by a prime number i.e. 2. It gives 13 as quotient and remainder is zero.

Step 3: Again we have to divide the quotient 13 by a prime number. Since 13 is a prime number, hence 13 will divide by itself only. So we divide 13 by 13.

Step 4. We got 1 as a quotient.

Hence, 52 = 2 x 2 x 13. So 52 **has only two prime factor i.e. 2 and 13.**

### 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 39**

In factor tree method, we can initiate the tree by choosing any two factors. Here we choose 3 and 13 as factors of 39.

Since both 3 and 13 are prime numbers and can not be further split.

Hence, we got 3 and 13 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.

**Factor Tree of 52**

We can initiate the tree by choosing any two factors. Here we choose 2 and 26 as factors of 52.

Further, we have to divide these nodes ( 2 & 26). So we split 26 into two factors 2 and 13.

Here we got, 2 and 13 as unique nodes. So 52 has two prime factors i.e. 2 and 13.

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

## Number of factors of 39

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

In our example, as we saw above 39 = 3 x 13 means 3 to the power 1 multiply 13 to the power 1

** Number of factors is = (power + 1)(power + 1)(power + 1)……….** = (1 + 1)(1 + 1) = 2 x 2 = 4

if we consider both positive and negative factors, then

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

Take another example, 52 = 2 x 2 x 13 means 2 to the power 2 multiply 13 to the power 1

Number of factors of 52 is = (2 + 1)(1 + 1) = 3 x 2 = 6 [ i.e. 1, 2, 4, 13, 26, 52 ]

and 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 39.

Try another number 34 for factors.

Take a another look of factorization on Quora.

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