Hello Guys !!

Here we are going to discuss, what are the **factors of 32** and **how many factors 32** **has** and what are the **factor ****pairs of 32**. Here are some methods, showing how to find the factors of 32.

Table of Contents

## Introduction To Factors Of 32

*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 8, it gives 32. Here 4 and 8 are positive factors of 32 or we multiply -2 to -16, it

gives 32. So -2 and -16 are negative factors of 32.

Hence, all the factors of 32 are : 1, 2, 4, 8, 16, 32

Similarly, the negative factors of 32 are : -1, -2, -4, -8, -16, -32

## Find The Factors Of 32 ?

Since factors of 32 are the numbers, which divides 32 completely without leaving remainder. So here we are

going to divide 32 by all numbers up to 32. 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’.

Take another example, Factors of 9

In above example of factors of 9, 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.

Hence, all the factors of 32 in above table 1 are : 1, 2, 4, 8, 16, 32

Similarly, negative factors of 32 are : -1, -2, -4, -8, -16, -32

## Factor Pairs Of 32

Factor Pair of 32 is a combination of two numbers, that product gives 32 when multiply these two numbers.

As we saw in above table, 1 multiply by 32 gives 32. So **(1, 32)** or (32, 1) is a factor pair of 32. Similarly, **(2, 16)** & **(4, 8)** are factor pairs of 32. Let us see how many factor pairs can be achieved –

1 x 32 = 32

2 x 16 = 32

4 x 8 = 32

8 x 4 = 32

16 x 2 = 32

32 x 1 = 32

Similarly, negative factor pairs of 32 can be written as follows –

-1 x -32 = 32

-2 x -16 = 32

-4 x -8 = 32

-8 x -4 = 32

-16 x -2 = 32

-32 x -1 = 32

Hence, 32 has 6 factor pairs.

## Prime Factors Of 32

Here we will discuss, mainly two methods of factorization to find Prime Factors of any number.

- Division Method
- Factor Tree Method

### Prime Factors of 32 By 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 32 and 180 .

In above example of 32,

Step 1 : First of all, we divide 32 by smallest prime number i.e. 2 and we got 16 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 16 by smallest prime number i.e. 2 and we got 8 as quotient.

Step 3: Repeat step 2 until we got 1 as a quotient.

Step 4: Here 2 used five times.

Hence, 32 = 2 x 2 x 2 x 2 x 2 = 2^{5 }So **32 has only one prime factor i.e. 2.**

and 180 = 2 x 2 x 3 x 3 x 5 = 2^{2} x 3^{2 }x 5. So **180 ^{ }has three prime factors i.e. 2, 3, 5.**

### Factor Tree Of 32

**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.

We can initiate the tree by choosing any two factors. Here we choose 4 and 8 as factors of 32, and we got the unique nodes. We may choose 2 and 16 as initial factors. Ultimately we got the same end nodes.

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

## How Many Factors Of 32 Are ?

To find the number of factors, we use **Division Method **. In our example, as we saw above 32 is 2^{5}

(2 to the power 5).

* Number of factors of 32 is = (power + 1) *= (5 + 1) = 6

and if we consider both positive and negative factors, then

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

Take another example, 48 = 2^{4} x 3^{1}

Number of factors of 48 is = (4 + 1) x (1 +1) = 5 x 2 = 10

and if we consider both positive and negative factors of 48, then

total no. of factors = 10 (positive) + 10 (negative) = 20

I hope, this step-by-step tutorial will be helpful to understand factorization method of 32.

Try next number => factors of 33

[…] we take another example prime factors of 32 = […]