# What are the Factors of 36

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What are the factors of 36 is the question that arises while dealing with factors of a number to be found. This can be achieved by using different methods like multiplication, division, and prime factorization.

## What are the Factors of 36?

Factors of 36 are the numbers that exactly divide 36 leaving the remainder zero. In simple words, it can be said if two numbers when multiplied give the product as 36 then the numbers are called factors of 36.

Factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Let’s pick a number called 3 from above

1. 36 ÷ 3 = 12
2. Here quotient = 12 and remainder = 0
3. If we multiply 12 and 3 product is 12 × 3 = 36
4. Therefore, 12 and 3 are factors of 36

### How to find factors of 36 using different methods

There are different methods to find factors of a number. By applying any of these methods it can be easy to find the factors of 36

### Multiplication method

In the multiplication method, we consider the numbers which when multiplied in pairs results to 36

Let’s see the multiplication process

1 × 36 = 36
2 × 18 = 36
3 × 12 = 36
4 × 9 = 36
6 × 6 = 36
9 × 4 =36 (Product repeats in reverse order multiplication )

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

### Division method

In the division method, we consider the numbers which exactly divide 36 with leaving a remainder.

Lets see the division process

36 ÷ 2 = 18
36 ÷ 3 = 12
36 ÷ 4 = 9
36 ÷ 6 = 6
36 ÷ 9 = 4
36 ÷ 12 = 3
36 ÷ 18 = 2

As 1 and itself are factors of any number 1 and 36 are also factors of 36
There all the numbers 1, 2, 3, 4, 6, 9, 12, and 36 are factors of the number 36.

### How to find factors of 36 by prime factorization method

In the prime factorization method, we consider the numbers written as a product of prime factors as prime factors of 36.

The following steps help in finding the prime factors of a number

Step1: Divide the given number 36 by the least prime number (2).
36 ÷ 2 = 18
Step2: If the resultant number is not divisible by this number (2) then, divide it using the next least prime number(3).
18 ÷ 2 = 9
Step3: As the resultant number 9 is not divisible by 2 we divide it by 3.
9 ÷ 3 = 3
Step4:  If the resultant number is not divisible by 3 divide it using the next least prime number 5.
3 ÷ 3 = 1

Considering all the above steps the prime factors of 36 are 2 × 2 × 3 × 3 => 2² × 3². The prime factors of 36 are 2 × 2 × 3 × 3 => 2² × 3².

## Factors of 36 in pairs and product form

From above, we know if the product of a pair of numbers is equal to 36 then the numbers are factors of 36. As the product of two negative numbers is positive there can be negative factors for the number 36. Thus we have a positive pair of factors of 36 and a negative pair of factors of 36.

### Positive pair of factors of 36

 Positive Factors of 36 Positive pair of factors of 36 1 × 36 (1, 36) 2 × 18 (2, 18) 3 × 12 (3, 12) 4 × 9 (4, 9) 6 × 6 (6, 6)

### Negative pair of factors of 36

 Positive Factors of 36 Positive pair of factors of 36 -1 × -36 (-1, -36) -2 × -18 (-2, -18) -3 × -12 (-3, -12) -4 × -9 (-4, -9) -6 × -6 (-6, -6)

## Factors of 36 solved example problems

Example1: How are the factors of 36 and 72 related?
Solution:

Factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Factors of 36 and 72 are related by common factors and all the factors of 36 are included in 72.
The common factors of 36 and 72 are1, 2, 3, 4, 6, 9, 12, 36.

Example2: Can you list the factors of 36 and its factor pair?
Solution:

The list of factors of 36 is 1, 2, 3, 4, 6, 9, 12, and 36.
List of factor pair of 36 are
Positive factor pair of 36: (1, 36), (2, 18), (3, 12), (4, 9), (6, 6)
Negative factor pair of 36: (-1, -36), (-2, -18), (-3, -12), (-4, -9), (-6, -6)

Example3: Find the average sum of all the prime factors of 36?
Solution:

Prime factors of 36 are 2 and 3
The average sum of prime factors of 36 is 2+3 = 5

Example4: Find the product of all the prime numbers of 36?
Solution:

Prime factors of 36 are 2 and 3.
The product of all the prime numbers of 36 is 2 × 3 = 6

Example5: Find the common factors of 36 and 42?
Solution:

The factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
The common factors of 36 and 42 are 1, 2, 3, and 6

FAQ’s

1. What are the prime factors of 36?
Ans: The prime factors of 36 are 2 and 3

2. How many factors does 36 have?
Ans: Number of factors of 36 have are 8

3. What are the common factors of 36?
Ans:
The common factors of 36 are positive factors of 36 and negative factors of 36.
Positive factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
Negative factors of 36 are -1, -2, -3, -4, -6, -9, -12 and -36

4. What numbers are the factors of 36?
Ans:
The numbers of factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36

5. What are the factors of 36 and 48?
Ans:
The factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

6. what are the factors of 36 in pairs
Ans:
Factors of 36 in pairs is (1, 36), (2, 18), (3, 12), (4, 9), (6, 6)

7. What are the common factors of 36 and 54?
Ans:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
Factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The common factors of 36 and 54 are 1, 2, 3, 6, and 9

8. What are the common factors of 36 and 90?
Ans:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
The common factors of 36 and 90 are 1, 2, 3, 6, and 9

9. What are the common factors of 36 and 40?
Ans:
Factors of 36 are 1, 2, 3, 4, 6, 9, 12 and 36
Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40.
The common factors of 36 and 40 are 1, 2, and 4

10. What is 36 as a product of prime factors?
Ans:
Prime factors of 36 in product form is 2² × 3²