Factors of 108

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The Factors of 108

In mathematical terms, 108 is said to be a composite number. In this chapter you will be made familiar with all the factors and factor pairs of 108 so it proves that your answer is solved correctly. That said, let’s get to know the factors for 108 that are as in the table given below:


Number

Factors Pairs of 108

108

1 x 108

108

2 x 54

108

3 x 36

108

4 x 27

108

6 x 18

108

9 x 12


Following are the factors of 108:


All Factors of 108

1

2

3

4

6

9

12

18

27

36

54

108


How Many Factors of 108 are There?

You should get the count for Factors from above, you will find that 108 has 12 positive factors and 12 negative factors. Hence, the total number of factors of 108 is 24.


What is the Definition of Factors of 108

The Factors of 108 consists of all the integers (positive as well as negative whole numbers) that we are able to can divide into 108. That being said, 108 divided by a Factor of 108 will be equivalent to another Factor of 108.


Prime Factorization of 108

A prime factorization is an outcome of factoring a number into a set of constituents which every member is a prime number. This is usually written by displaying 108 as a product of its prime factors. For 108, this outcome will be:

This is also called the prime factorization; the smallest prime number in this series is defined as the smallest prime factor.

Prime factorization: 108 = 2 x 2 x 3 x 3 x 3, this can also be mathematically written 108 = 2² x 3³.


Because the factors of 108 are all the numbers (positive and negative numbers) that are evenly divided into 108, we simply require to divide 108 by all numbers up to 108 to find out which ones lead up to an even quotient. Let’s perform the operation of division to find out which calculations outcomes in even quotient:


How to Find The Factors of 108

Division

Quotient

108 ÷ 1

108

108 ÷ 2

54

108 ÷ 3

36

108 ÷ 4

27

108 ÷ 6

18

108 ÷ 9

12

108 ÷ 12

9

108 ÷ 18

6

108 ÷ 27

4

108 ÷ 36

3

108 ÷ 54

2

108 ÷ 108

1


Positive Factors of 108

The Positive Factors of 108 are thus all the mathematical numbers we used to divide to obtain an even number. Below are all the positive factors of 108 arranged in numerically ascending order:

1

2

3

4

6

9

12

18

27

36

54

108


Negative Factors of 108

There are also negative numbers for factors of 108. Hence, all the positive factors of 108 can be transformed to negative numbers. Below are all the negative factors of 108 arranged in numerically ascending order:

-1

-2

3

-4

-6

-9

-12

-18

-27

-36

-54

-108.


How to Find Negative Factors of 108 (-108)

First find all the positive factors, and then replicate them prefixing a minus sign before each one (functionally multiplying them by -1). This results in negative factors of 108.


Solved Examples

Example1: Determine the sum of all the factors of 108, including 108?

Solution: factors of 108 are as given:

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 

Now, Sum up all the factors

1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280

Hence the total of all factors of the number 108 = 280


Example2:

Evaluate the mean of all the factors of the number 108. Take the answer in round off to two decimal places.

Solution:

Factors of 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108 

Sum = 1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 27 + 36 + 54 + 108 = 280

In order to find out the mean, we will divide sum of factors with total number of factors, with which we get,

280/12 = 23.33.

FAQ (Frequently Asked Questions)

Q1. Is 108 a Composite Number?

Answer: Yes! 108 is a composite number, since it is the product of two positive numbers except 1 and itself.

Q2. Is 108 a Square Number?

Answer: No! 108 is NOT a square number, because the square root of 108 is (10.39) which is not an integer. But 108 is a whole number. And remember that only integers and whole numbers can be factors.

Q3. What is the Greatest Common Factor of 108?

Answer: The greatest common factor also referred to as the highest common factor of two numbers can be identified by establishing comparison of the two numbers and taking the highest common prime factor, the prime factorization. The GCF is 1 if there is no common factor. The GCF is part of the common prime factors of two numbers.

Q4. What is the Rule of Divisibility to Find Factors?

Answer: Divisibility implies to a given integer number that is being divisible for a given divisor. The divisibility rules are a roundup mechanism to identify what is or isn't divisible. This includes rules about even number and odd number factors. This example is deliberated to enable the student to approximate the status of a given number without performing calculation.