Here we are going to discuss, what are the **factors of 51** and how many factors 51 has and what are the **factors of 51 in pairs **. Here are some methods, showing how to find the factors of 51.

*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 17, it gives 51. Here 3 and 17 are positive factors of 51 or we multiply -1 to -51, it gives 51. So -1 and -51 are negative factors of 51.

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## What are the Factors of 51 ?

Since factors of 51 are the numbers, which divides 51 completely without leaving remainder. So here we are

going to divide 51 by all numbers up to 51. 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 17 appears in column ‘A’, which has already been came in column ‘B’.

Hence, positive factors of 51 in above table are : 1, 3, 17, 51

Similarly, negative factors of 51 are : -1, -3 -17, -51

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 51

As we saw in above table, 1 multiply by 51 gives 51. So (1, 51) or (51, 1) is a factor pair of 51.

Similarly, (3, 17) is another factor pairs of 51.

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

## Methods of Prime Factors of 51

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 51 and 68**

In above example of 51

Step 1 : First of all, we divide 51 by smallest prime number i.e. 2, but it doesn’t divide completely. So try next prime number 3. It gives 17 as quotient.

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

Step 2: Since 17 is a prime number, hence it will divide by itself only.

Hence, 51 = 3 x 17. So** 51 has two prime factor i.e. 3 and 17.**

In second example of 68

Step 1 : First of all, we divide 68 by smallest prime number i.e. 2, it gives 34 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 34 by a prime number i.e. 2. It gives 17 as quotient and remainder is zero.

Step 3: Again we have to divide the quotient 17 by a prime number. Since 17 is a prime number, hence 17 will divide by itself only. So we divide 17 by 17.

Step 4. We got 1 as a quotient.

Hence, 68 = 2 x 2 x 17. So **68 has only two prime factor i.e. 2 and 17.**

### 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 51**

In factor tree method, we can initiate the tree by choosing any two factors. Here we choose 3 and 17 as factors of 51.

Since both 3 and 17 are prime numbers and can not be further split.

Hence, we got 3 and 17 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 68**

We can initiate the tree by choosing any two factors. Here we choose 4 and 17 as factors of 68.

Further, we have to divide these nodes ( 4 & 17). So we split 4 into two factors 2 and 2.

Here we got, 2 and 17 as unique nodes. So 68 has two prime factors i.e. 2 and 17.

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

## Number of factors of 51

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

In our example, as we saw above 51 = 3 x 17 = 3 x 17 means 3 to the power 1 multiply 17 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, 68 = 2 x 2 x 17 means 2 to the power 2 multiply 17 to the power 1

Number of factors of 68 is = (2 + 1)(1 + 1) = 3 x 2 = 6

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 51.

Try another number 28 for factors.

Take a another look of factorization on Quora.

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