# Factors of 36 in pair

Factors of 36 in pair are (1, 36) , (2, 18) , (3, 12) , (4, 9) and (6, 6)

#### How to find factors of a number in pair

 1.   Steps to find factors of 36 in pair 2.   What is factors of a number in pair? 3.   What are Factors? 4.   Frequently Asked Questions 5.   Examples of factors in pair

### Example: Find factors of 36 in pair

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 ) .

#### Introduction to factor pairs

Factor pair in mathematics is defined as all factors of a given number which when written in pair and multiplied gives the original number. Every natural number is a product of atleast one factor pair. Eg- Factors of 36 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36. So, factors of 36 in pair are (1,36), (2,18), (3,12), (4,9), (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.

#### Steps to find Factors of 36

• Step 1. Find all the numbers that would divide 36 without leaving any remainder. Starting with the number 1 upto 18 (half of 36). The number 1 and the number itself are always factors of the given number.
36 ÷ 1 : Remainder = 0
36 ÷ 2 : Remainder = 0
36 ÷ 3 : Remainder = 0
36 ÷ 4 : Remainder = 0
36 ÷ 6 : Remainder = 0
36 ÷ 9 : Remainder = 0
36 ÷ 12 : Remainder = 0
36 ÷ 18 : Remainder = 0
36 ÷ 36 : Remainder = 0

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

• Is 36 a composite number?

Yes 36 is a composite number.

• Is 36 a prime number?

No 36 is not a prime number.

• What is the mean of factors of 36?

Factors of 36 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36. therefore mean of factors of 36 is (1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36) / 9 = 10.11.

• What do you mean by proper divisors?

A number x is said to be the proper divisor of y if it divides y completely, given that x is smaller than y.

• What do you mean by improper divisors?

An improper divisor of a number is the number itself apart from this any divisor of a given number is a proper divisor.

#### Examples of Factors

Rustom has been assigned the following tasks by the teacher:
- Finding out all positive factors of 36.
- Writing all prime factors of 36.
- Writing all the possible factors of 36 in pair.
Help him in writing all these.

Positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Prime factors of 36 are 2, 2, 3, 3.
Factors of 36 in pair are (1,36), (2,18), (3,12), (4,9), (6,6).

What are the pair factors of 36?

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Hence, the factors of 36 in pair are (1,36), (2,18), (3,12), (4,9), (6,6).

Can you help Sammy list the factors of 36 and also find the factor pairs?

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 36 in pair are (1,36), (2,18), (3,12), (4,9), (6,6).

The area of a rectangle is 36 square meters. List all the possible combinations possible for length and breadth in which a designer can design out all the combinations.

For the possible combinations possible for length and breadth in which a designer can design out all the rectangles can be calculated by calculating the factors of 36 in pair. So, the possible combinations (1,36), (2,18), (3,12), (4,9), (6,6).

Help Diji in finding factors of 36 by Prime Factorization method and then sorting factors of 36 in pairs.

Prime factorization of 36 is 2 x 2 x 3 x 3. Factors of 36 in pair can be written as (1,36), (2,18), (3,12), (4,9), (6,6).

Write the smallest prime factor of 36.

Smallest prime factor of 36 is 2.

Write the largest prime factor of 36.

Largest prime factor of 36 is 3.

Diji wants to write all the negative factors of 36. Can you help Diji in doing the same?

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