# [Maths Class Notes] on Factors of 36 Pdf for Exam

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.

### Prime Number

Prime numbers are whole numbers that are divisible by the number 1 and the number itself. So they have just two factors. For example 2,3,5,7,11… are the beginning prime numbers. 1 is neither a prime number nor a composite number. The prime number was discovered by Eratosthenes in around 275-194 B.C. He took the example of a sieve to filter out the prime numbers and drain out composite numbers from a list of natural numbers.

### Co-Prime Numbers

Two numbers are said to be co-prime or mutually prime if and only if their common factor or only positive integer that is divisor for both of them is 1. In other words, their highest common factor is always 1.

For example, 21 and 22.
Factors of 21 are 1, 3, 7, 21 and factors of 22 are 1, 2, 11 and 22.

1. Prime numbers between 1 and 100 are more than the prime numbers between 101-200.

2. The only even Prime number is 2, the rest of the prime numbers are odd.

3. Two numbers are always coprime to one another.

4. No prime number which is greater than 5 ends with the number 5.

### Factors of 36

The factors of the number 36 are the numbers that are multiplied together to get the original number 36. Since the number 36 is a composite number and not a prime number, there are many other factors besides the 1 and the number itself. Therefore, the  36 elements are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

### Prime Factor and Prime Factorisation of Number 36

36 is divisible by the prime number 2 and becomes 18. If you repeat the same procedure again, the resulting value will be 9. Furthermore, 9 is divisible by the prime number 3, and the result after division is 3 which is a prime number and cannot be divided any further. number. Therefore, the prime factors of 36 are 2, 2, 3, and 3.

The method of writing a number as the product of 36 prime factors is called the 36 prime factorizations. To find the 36 prime factors, divide them by the smallest prime number, 2. If it cannot be further divided by 2, divide by the next prime number, 3, and continue this process until the final product is 1. This is called the prime factorization of numbers, and the  36 increments are shown below.

Step 1: Divide 36 with 2

36 ÷ 2 = 18

Step 2:  Again divide 18 with 2

18 ÷ 2 = 9

Step 3: Since 9 is not divisible by 2, our next prime number is 3

9 ÷ 3 = 3

Step 4:  Finally at the last step divide 3 with 3 to get 1.

3 ÷ 3 = 1

We can see here that the prime factors of 36 will be 2 × 2 × 3 × 3 i.e. 2^2 × 3^2.

### Factors of 36 Definition

We know that the factor of a number divides the number completely if we talk about the number 36, the number 36 is composite and it can be presented as a unique product of primes, which is actually prime factorization. There is more than one factor for a number like 36;  however, there is always one way of representing the number as a product of prime which is why prime factorization is called a unique product of primes. Now, let’s write the various factors of 36:

36 = 36 x 1

= 18 x 2

= 12 x 3 or 3 x 12

= 9 x 4  or 4 x 9

=  6 x 6

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

-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 Factors 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.

Example 3: If 144 is One of the Multiples of 36, then Write its Factors.

Solution:

The factors of 72 are the same, with additional factors of 72 and 144. We can write the factor of 72 as 1, 2, 3, 4, 6, 9, 12, 18, 36, 72, and 144.

### Quiz Time

1. Find the factors for 48

2. Find the factors for 37