 # Factors of 36

## What are the Factors of 36

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the given number. For example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. On this page, we will study the factors of 36 definitions, how to find the factors of 36 and examples.

### Factors of 36 Definition

The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors can be either positive or negative integers.

Factors of 36 are all the integers that can evenly divide the given number 36.

Now let us find the factors of 36.

### How to Find the Factors of 36?

According to the definition of factors of 36 we know that factors of 36 are all the positive or negative integers which divide the number 36 completely. So let us simply divide the number 36 by every number which completely divides 36 in ascending order till 36.

36 ÷ 1 = 36

36 ÷ 2 = 18

36 ÷ 3 = 12

36 ÷ 4 = 9

36 ÷ 6 = 6

36 ÷ 9 = 4

36 ÷ 12 = 3

36 ÷ 18 = 2

36 ÷ 36 = 1

So the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, and 36.

We know that factors also include negative integers hence we can also have,

list of negative factors of 36 :-1, -2, -3, -4, -6, -9, -12, -18, and -36.

## Factors of 36 can be listed as follows.

 Positive Factors of 36 1, 2, 3, 4, 6, 9, 12, 18, and 36 Negative Factors of 36 – 1, – 2, – 3, – 4, – 6, – 9, – 12, – 18, and – 36

Hence 36 have total 9 positive factors and 9 negative factors.

### Factors Pairs of 36

Factor Pairs of 36 are combinations of two factors that when multiplied together give 36.

List of all the Positive Factor Pairs of 36

1 x 36 = 36

2 x 18 = 36

3 x 12 = 36

4 x 9 = 36

6 x 6 = 36

9 x 4 = 36

12 x 3 = 36

18 x 2 = 36

36 x 1 = 36

As we know that Factors of 36 include negative integers too.

List of all the Negative Factor Pairs of 36:

-1 x -36 = 36

-2 x -18 = 36

-3 x -12 = 36

-4 x -9 = 36

-6 x -6 = 36

-9 x -4 = 36

-12 x -3 = 36

-18 x -2 = 36

-36 x -1 = 36

### Prime Factorization of 36

According to the prime factor definition we know that the prime factor of a number is the product of all the factors that are prime( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 36.

Or the other way to find the prime factorization of 36 is by prime factorization or by factor tree.

### How To Calculate Prime Factorization of 36?

To calculate the prime factorization of 36, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 36

Step 1: Divide 36 with 2

2 ÷ 36 = 18

Step 2: Again divide 18 with 2

2 ÷ 18 = 9

Step 3: Now 9 is no more divisible by 2, move to the next prime number i.e. 3

3 ÷ 9 = 3

Step 4: At last, divide 3 with 3 to get 1.

3 ÷ 3 = 1

From the above steps, we get a prime factor of 36 as 2 × 2 × 3 × 3 i.e. 22 × 32

And also,

Here is the factor tree representing prime factors of 36.

### Solved Examples

Example 1: Write down the factors of 16.

Solution:

16 ÷ 1 = 16

16 ÷ 2 = 8

16 ÷ 4 = 4

16 ÷ 8 = 2

16 ÷ 16 = 1

Therefore the factors of 16 are 1, 2, 4, 8 and 16.

Example 2: Write down the factors of 68.

Solution:

68 ÷ 1 = 68

68 ÷ 2 = 34

68 ÷ 4 = 17

68 ÷ 17 = 4

68 ÷ 34 = 2

68 ÷ 68 = 1

Therefore the factors of 16 are 1, 2, 4, 17, 34 and 68.

### Quiz time

1. Find the factors for 48

2. Find the factors for 37

1. How to calculate factors of large numbers?

We can calculate factors of large numbers by the trial division method. We first try to divide the number by the smallest number such that it should completely divide the number. The result is again divided by the next number. This step is continued till we get the quotient as 1. At last, we will get all the factors of a given number. For example, let us factorize 100

• 100 ÷ 2 = 50; first factor is 2

• 100 ÷ 4 = 25;second factor is 4

• 100 ÷ 5 = 20;third factor is 5

• 100 ÷ 10 = 10;fourth factor is 10

• 100 ÷ 20 = 5;fifth factor is 20

• 100 ÷ 25 = 4;sixth factor is 25

• 100 ÷ 50 = 2;seventh factor is 50

• 100 ÷ 100 = 1;eighth factor is 100

So the factors of 100 are 2, 4, 5, 10, 20, 25, 50 and 100.