# Factors of 108 in pair

Factors of 108 in pair are (1, 108) , (2, 54) , (3, 36) , (4, 27) , (6, 18) and (9, 12)

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

 1.   Steps to find factors of 108 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 108 in pair

Factor Pair Pair Factorization
1 and 108 1 x 108 = 108
2 and 54 2 x 54 = 108
3 and 36 3 x 36 = 108
4 and 27 4 x 27 = 108
6 and 18 6 x 18 = 108
9 and 12 9 x 12 = 108

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 108. They are called negative pair factors.

Hence, the negative pairs of 108 would be ( -1 , -108 ) .

#### What does factor pairs in mathematics mean?

In mathematics, factor pair of a number are all those possible combination which when multiplied together give the original number in return. Every natural number is a product of atleast one factor pair. Eg- Factors of 108 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 108. So, factors of 108 in pair are (1,108), (2,54), (3,36), (4,27), (6,18), (9,12).

#### What is the definition of factors?

In mathematics, factors are number, algebraic expressions which when multiplied together produce desired product. A factor of a number can be positive or negative.

#### Properties of Factors

• Each number is a factor of itself. Eg. 108 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 108.
• Every number is a factor of zero (0), since 108 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, 27, 36, 54, 108 are exact divisors of 108.
• Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. Each factor divides 108 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, 27, 36, 54, 108 are all less than or equal to 108.

#### Steps to find Factors of 108

• Step 1. Find all the numbers that would divide 108 without leaving any remainder. Starting with the number 1 upto 54 (half of 108). The number 1 and the number itself are always factors of the given number.
108 ÷ 1 : Remainder = 0
108 ÷ 2 : Remainder = 0
108 ÷ 3 : Remainder = 0
108 ÷ 4 : Remainder = 0
108 ÷ 6 : Remainder = 0
108 ÷ 9 : Remainder = 0
108 ÷ 12 : Remainder = 0
108 ÷ 18 : Remainder = 0
108 ÷ 27 : Remainder = 0
108 ÷ 36 : Remainder = 0
108 ÷ 54 : Remainder = 0
108 ÷ 108 : Remainder = 0

Hence, Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108

• Is 108 a composite number?

Yes 108 is a composite number.

• Is 108 a prime number?

No 108 is not a prime number.

• What is the mean of factors of 108?

Factors of 108 are 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 27 , 36 , 54 , 108. therefore mean of factors of 108 is (1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108) / 12 = 23.33.

• 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 108.
- Writing all prime factors of 108.
- Writing all the possible factors of 108 in pair.
Help him in writing all these.

Positive factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Prime factors of 108 are 2, 2, 3, 3, 3.
Factors of 108 in pair are (1,108), (2,54), (3,36), (4,27), (6,18), (9,12).

What are the pair factors of 108?

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. Hence, the factors of 108 in pair are (1,108), (2,54), (3,36), (4,27), (6,18), (9,12).

Can you help Sammy list the factors of 108 and also find the factor pairs?

Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Factors of 108 in pair are (1,108), (2,54), (3,36), (4,27), (6,18), (9,12).

The area of a rectangle is 108 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 108 in pair. So, the possible combinations (1,108), (2,54), (3,36), (4,27), (6,18), (9,12).

Help Diji in finding factors of 108 by Prime Factorization method and then sorting factors of 108 in pairs.

Prime factorization of 108 is 2 x 2 x 3 x 3 x 3. Factors of 108 in pair can be written as (1,108), (2,54), (3,36), (4,27), (6,18), (9,12).

Write the smallest prime factor of 108.

Smallest prime factor of 108 is 2.

Write the largest prime factor of 108.

Largest prime factor of 108 is 3.

Diji wants to write all the negative factors of 108. Can you help Diji in doing the same?

Negative factors of 108 are -1, -2, -3, -4, -6, -9, -12, -18, -27, -36, -54, -108.