Here we are going to discuss, what are the **factors of 56** and how many factors 56 has and what are the **factor pairs of 56**. Here are some methods, showing how to find the factors of 56.

*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 14, it gives 56. Here 4 and 14 are positive factors of 56 or we multiply -7 to -8, it gives 56. So -7 and -8 are negative factors of 56.

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## What are the Factors of 56 ?

Since factors of 56 are the numbers, which divides 56 completely without leaving remainder. So here we are

going to divide 56 by all numbers up to 56. 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 8 appears in column ‘A’, which has already been came in column ‘B’.

Hence, all the factors of 56 in above table are : 1, 2, 4, 7, 8, 14, 28, 56

Similarly, negative factors of 56 are : -1, -2, -4, -7, -8, -14, -28, -56

Take another example, Factors of 49

In 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 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 56

As we saw in above table, 1 multiply by 56 gives 56. So (1, 56) or (56, 1) is a factor pair of 56.

Similarly, (2, 28), (4, 14) and (7, 8) are another factor pairs of 56.

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

## Methods of Prime Factors of 56

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 56 and 96

In above example of 56,

Step 1 : First of all, we divide 56 by smallest prime number i.e. 2, it gives 28 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 28 by a prime number i.e. 2. It gives 14 as quotient and remainder is zero.

Step 3: Again we have to divide the quotient 14 by a prime number i.e. 2. It gives 7 as quotient and remainder is zero.

Step 4: Since 7 is a prime number, hence 7 will divide by itself only. So we divide 7 by 7. We got 1 as a quotient.

Hence, 56 = 2 x 2 x 2 x 7. So 56** has only two prime factor i.e. 2 and 7.**

In second example of 96

Step 1 : First of all, we divide 96 by smallest prime number i.e. 2 and we got 48 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 divide the quotient 48 by smallest prime number i.e. 2 and we got 24 as quotient. (Repeat step 2 until we got 1 as a quotient.)

Again we divide the quotient 24 by smallest prime number i.e. 2, we got 12 as quotient.

Again we divide 12 by smallest prime number i.e. 2, we got 6 as quotient.

Again we divide 6 by smallest prime number i.e. 2, we got 3 as quotient.

Since 3 is a prime number, it will only divide by self. We got 1 as quotient.

Hence, 96 = 2 x 2 x 2 x 2 x 2 x 3 = 2^{5} x 3

So 96 has two prime factor i.e. 2 & 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 56**

In First Tree ( see above figure), We can initiate the tree by choosing any two factors. Here we choose 4 and 14 as factors of 56.

Further, we have to divide these nodes ( 4 & 14). So we split 4 into two factors 2 and 2. And 14 into 2 and 7.

Here we got, 2 and 7 as unique nodes. So 56 has two prime factors i.e. 2 and 7.

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

Similarly we can make other factor trees of 56 (as second example in above figure)

## Number of factors of 56

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

In our example, as we saw above 56 = 2 x 2 x 2 x 7 means 2 to the power 3 multiply 7 to the power 1

** Number of factors is = (power + 1)(power + 1)(power + 1)……….** = (3 + 1)(1 + 1) = 4 x 2 = 8

if we consider both positive and negative factors, then

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

Take another example, 96 = 2 x 2 x 2 x 2 x 2 x 3 = 2^{5} x 3

Number of factors of 96 is = (5 + 1)(1 + 1) = 6 x 2 =12

and if we consider both positive and negative factors, then

total no. of factors = 12 (positive) + 12 (negative) = 24

I hope, this step-by-step tutorial will be helpful to understand factorization method of 56.

Try another number 68 for factors.

Take a new look of factorization on Quora.

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