## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{110,220}/_{6}

#### The number above the bar is the numerator: 110,220

#### The number below the bar is the denominator: 6

#### The fraction bar means that the two numbers are dividing themselves:

^{110,220}/_{6} = 110,220 ÷ 6

#### Divide the numerator by the denominator to get fraction's value:

Value = 110,220 ÷ 6

### Introduction. Percent

#### 'Percent (%)' means 'out of one hundred':

#### p% = p 'out of one hundred',

#### p% = ^{p}/_{100} = p ÷ 100

### Note:

#### The fraction ^{100}/_{100} = 100 ÷ 100 = 100% = 1

#### Multiply a number by the fraction ^{100}/_{100},

... and its value doesn't change.

## To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

#### To calculate the greatest common factor, we build the prime factorization of the two numbers.

### Integer numbers prime factorization:

#### Prime Factorization of a number: finding the prime numbers that multiply together to make that number.

#### 110,220 = 2^{2} × 3 × 5 × 11 × 167;

110,220 is not a prime, is a composite number;

#### 6 = 2 × 3;

6 is not a prime, is a composite number;

** Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself. *

* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

### Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

#### Multiply all the common prime factors, by the lowest exponents (if any).

#### gcf, hcf, gcd (110,220; 6) = 2 × 3 = 6

### Divide both the numerator and the denominator by their greatest common factor.

^{110,220}/_{6} =

^{(22 × 3 × 5 × 11 × 167)}/_{(2 × 3)} =

^{((22 × 3 × 5 × 11 × 167) ÷ (2 × 3))} / _{((2 × 3) ÷ (2 × 3))} =

^{(2 × 5 × 11 × 167)}/_{1} =

^{18,370}/_{1} =

#### 18,370

#### When the denominator is 1 it can be omitted.

## The fraction is now reduced to the lowest terms.

### 18,370 = ^{18,370}/_{1} is an improper fraction.

#### An improper fraction: numerator larger than denominator.

## Rewrite the end result, continued below...

## Rewrite the end result:

### As an improper fraction

(denominator = 1):

#### 18,370 = ^{18,370}/_{1}

### As a percentage:

#### 18,370 =

#### 18,370 × ^{100}/_{100} =

^{(18,370 × 100)}/_{100} =

^{1,837,000}/_{100} =

#### 1,837,000%

#### In other words:

#### 1) Calculate fraction's value.

#### 2) Multiply that number by 100.

#### 3) Add the percent sign % to it.

## Final answer

continued below...