## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{2,166,887,928}/_{32}

#### The number above the bar is the numerator: 2,166,887,928

#### The number below the bar is the denominator: 32

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

^{2,166,887,928}/_{32} = 2,166,887,928 ÷ 32

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

Value = 2,166,887,928 ÷ 32

### 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.

#### 2,166,887,928 = 2^{3} × 3 × 149 × 605,953;

2,166,887,928 is not a prime, is a composite number;

#### 32 = 2^{5};

32 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 (2,166,887,928; 32) = 2^{3} = 8

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

^{2,166,887,928}/_{32} =

^{(23 × 3 × 149 × 605,953)}/_{25} =

^{((23 × 3 × 149 × 605,953) ÷ 23)} / _{(25 ÷ 23)} =

^{(3 × 149 × 605,953)}/_{22} =

^{270,860,991}/_{4}

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

^{270,860,991}/_{4} is an improper fraction.

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

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

## Rewrite the fraction:

### As a mixed number (mixed fraction):

#### A mixed number (mixed fraction): a whole number and a proper fraction, of the same sign.

#### A proper fraction: numerator smaller than denominator.

#### 270,860,991 ÷ 4 = 67,715,247 and remainder = 3 =>

#### 270,860,991 = 67,715,247 × 4 + 3 =>

^{270,860,991}/_{4} =

^{(67,715,247 × 4 + 3)} / _{4} =

^{(67,715,247 × 4)} / _{4} + ^{3} / _{4} =

#### 67,715,247 + ^{3}/_{4} =

#### 67,715,247 ^{3}/_{4}

### As a decimal number:

#### 67,715,247 ^{3}/_{4} =

#### 67,715,247 + ^{3}/_{4} =

#### 67,715,247 + 3 ÷ 4 =

#### 67,715,247.75

### As a percentage:

#### 67,715,247.75 =

#### 67,715,247.75 × ^{100}/_{100} =

#### ^{6,771,524,775}/_{100} =

#### 6,771,524,775%

#### 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...