Here we are going to discuss, what are the **factors of 52** and how many factors 52 has and what are the **factors of 52 in pairs**. Here are some methods, showing how to find the factors of 52.

*Actually, Factor is a number that divides any number completely without leaving the 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 13, it gives 52. Here 4 and 13 are positive factors of 52 or we multiply -2 to -26, it gives 52. So -2 and -26 are negative factors of 52.

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## What are the Factors of 52 ?

Since factors of 52 are the numbers, which divides 52 completely without leaving the remainder. So here we are

going to divide 52 by all numbers up to 52. 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 52 in above table are : 1, 2, 4, 13, 26, 52

Similarly, negative factors of 52 are : -1, -2, -4, -13, -26, -52

Take another example, **Factors of 49 **

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

when 7 comes, because on dividing by 7, it produces the same number (7 = 7)

So we have to stop the process when any element comes in both columns at the 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 52

As we saw in the above table, 1 multiply by 52 gives 52. So (1, 52) or (52, 1) is a factor pair of 52.

Similarly, (2, 26), (4, 13) are another factor pairs of 52.

In example of 49 ; (1, 49) or (49, 1) and (7, 7) are factor pairs.

## Methods of Prime Factors of 52

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 the quotient is not exactly divisible by the

smallest prime number, choose the 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 the 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 used to divide.

Take the example of **factors of 52 and 78 **

**In the above example of 52 **

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

Step 3 : Since 13 is a prime number, hence it will divide by itself only.

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

**In the second example, factors of 78**

Step 1 : First of all, we divide 78 by the smallest prime number i.e. 2 and we got 39 as quotient and the remainder is zero. (Note – if remainder will not zero, means doesn’t divide exactly, try next prime number to divide)

Step 2: Again we divide the quotient 39 by the smallest prime number i.e. 2, but 2 doesn’t divide 15 exactly. So we try to divide the next prime number i.e. 3 and we got 13 as quotient.

Step 3: Since 13 is a prime number, hence it will divide by itself only.

Hence, 78 = 2 x 3 x 13, So **78 has three prime factors i.e. 2, 3 & 13 **

### Method #2 (Factor Tree Method)

**Step 1 :** Write a number as the 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 roots)

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

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

**Factor Tree of 52**

In the factor tree method, 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). Since 2 is a prime number and can’t be split anymore. So we split 26 into two factors 2 and 13.

We got 2, 2 and 13 as end nodes.

Since both 2 and 13 are prime numbers and can not be further split.

Hence, we got 2 and 13 unique nodes.

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

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

**Factor Tree of 78**

We can initiate the tree by choosing any two factors. Here we choose 2 and 39 as factors of 78 as initial nodes.

Further, we divide 39 into two parts i.e 3 and 13.

Hence we got end nodes as 2, 3 and 13.

since all three end nodes are unique. So prime factors of 75 are : 2, 3 and 13.

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

## Number of factors of 52

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

In our example, as we saw above 52 = 2 x 2 x 13 = 2^{2} x 13 means 2 to the power 2 multiply 13 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, 78 = 2 x 3^{ }x 13 means 2 to the power 1 multiply 3 to the power 1 multiply 13 to the power 1

Number of factors of 60 is = (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 [ i.e. 1, 2, 3, 6, 13, 26, 39, 78 ]

and if we consider both positive and negative factors, then

total no. of factors = 8 (positive) + 8 (negative) = 16

I hope, this step-by-step tutorial will be helpful to understand factorization method of 52.

Try another number 45 for factors.

[…] Factors of 52 ( Best 3 Methods ) […]