# Factors of 36

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

#### How to find factors of a number

 1.   Find factors of 36 using Division Method 2.   Find factors of 36 using Prime Factorization 3.   Find factors of 36 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 36

• Divide 36 by 1: 36 ÷ 1 : Remainder = 0
• Divide 36 by 2: 36 ÷ 2 : Remainder = 0
• Divide 36 by 3: 36 ÷ 3 : Remainder = 0
• Divide 36 by 4: 36 ÷ 4 : Remainder = 0
• Divide 36 by 6: 36 ÷ 6 : Remainder = 0
• Divide 36 by 9: 36 ÷ 9 : Remainder = 0
• Divide 36 by 12: 36 ÷ 12 : Remainder = 0
• Divide 36 by 18: 36 ÷ 18 : Remainder = 0
• Divide 36 by 36: 36 ÷ 36 : Remainder = 0

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

#### 2. Steps to find factors of 36 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 36 using the division method, follow these steps:

• Step 1. Start dividing 36 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 36, which is 2. Divide 36 by 2 to obtain the quotient (18).
36 ÷ 2 = 18
• Step 3. Repeat step 1 with the obtained quotient (18).
18 ÷ 2 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

So, the prime factorization of 36 is, 36 = 2 x 2 x 3 x 3.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 36 as shown below:

So, the prime factorization of 36 is, 36 = 2 x 2 x 3 x 3.

#### 3. Find factors of 36 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 36 would be the two numbers which, when multiplied, give 36 as the result.

The following table represents the calculation of factors of 36 in pairs:

Factor Pair Pair Factorization
1 and 36 1 x 36 = 36
2 and 18 2 x 18 = 36
3 and 12 3 x 12 = 36
4 and 9 4 x 9 = 36
6 and 6 6 x 6 = 36

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 36. They are called negative pair factors.

Hence, the negative pairs of 36 would be ( -1 , -36 ) , ( -2 , -18 ) , ( -3 , -12 ) , ( -4 , -9 ) and ( -6 , -6 ) .

#### How can we define factors?

In mathematics a factor is a number which divides into another without leaving any remainder. Or we can say, any two numbers that multiply to give a product are both factors of that product. It can be both positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 36 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 36.
• Every number is a factor of zero (0), since 36 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 4, 6, 9, 12, 18, 36 are exact divisors of 36.
• Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Each factor divides 36 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 3, 4, 6, 9, 12, 18, 36 are all less than or equal to 36.

• Which is the smallest prime factor of 36?

Smallest prime factor of 36 is 2.

• Is 36 a perfect square?

Yes 36 is a perfect square.

• What are five multiples of 36?

First five multiples of 36 are 72, 108, 144, 180, 216.

• What is prime factorization of 36?

Prime factorization of 36 is 2 x 2 x 3 x 3.

• What are factors of 36?

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

• How do you find factors of a negative number? ( eg. -36 )?

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

• Is 36 a whole number?

Yes 36 is a whole number.

• Which is greatest factor of 36?

The greatest factor of 36 is 18.

• What are the prime factors of 36?

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Prime factors of 36 are 2, 2, 3, 3.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 36. Can you help her?

Prime factors of 36 are 2, 2, 3, 3.
Hence, the product of prime factors of 6.

Can you help Rubel to find out the product of the even factors of 36?

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Even factors of 36 are 2, 4, 6, 12, 18, 36.
Hence, product of even factors of 36 is; 2 x 4 x 6 x 12 x 18 x 36 = 373248.

Joy wants to calculate mean of all the factors of 36. Help him in finding the mean of 36.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 36 is 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = 91.
Hence, the mean of factors of 36 is 91 ÷ 9 = 10.11.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 36? Help her in writing all the factors.

Positive factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Negative factors are -1, -2, -3, -4, -6, -9, -12, -18, -36.

How many factors are there for 36?

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
So there are in total 9 factors.

Joey wants to write all the prime factors of 36 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 36 are 2, 2, 3, 3.
So in exponential form it can be written as 22 x 32.

Kevin has been asked to write 8 factor(s) of 36. Can you predict the answer?

8 factor(s) of 36 are 1, 2, 3, 4, 6, 9, 12, 18.