## Reduce: ^{120}/_{640,588}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{120}/_{640,588}

#### The number above the bar is the numerator: 120

#### The number below the bar is the denominator: 640,588

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

^{120}/_{640,588} = 120 ÷ 640,588

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

Value = 120 ÷ 640,588

### 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.

#### 120 = 2^{3} × 3 × 5;

120 is not a prime, is a composite number;

#### 640,588 = 2^{2} × 13 × 97 × 127;

640,588 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 (120; 640,588) = 2^{2} = 4

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

^{120}/_{640,588} =

^{(23 × 3 × 5)}/_{(22 × 13 × 97 × 127)} =

^{((23 × 3 × 5) ÷ 22)} / _{((22 × 13 × 97 × 127) ÷ 22)} =

^{(2 × 3 × 5)}/_{(13 × 97 × 127)} =

^{30}/_{160,147}

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

^{30}/_{160,147} is a proper fraction.

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

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

## Rewrite the end result:

### As a decimal number:

^{30}/_{160,147} =

#### 30 ÷ 160,147 ≈

#### 0.000187327892 ≈

#### 0

### As a percentage:

#### 0.000187327892 =

#### 0.000187327892 × ^{100}/_{100} =

#### ^{0.01873278925}/_{100} =

#### 0.01873278925% ≈

#### 0.02%

#### 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...

## Final answer:

:: written in three ways ::

## As a proper fraction

(numerator smaller than denominator):

^{120}/_{640,588} = ^{30}/_{160,147}

## As a decimal number:

^{120}/_{640,588} ≈ 0.000187327892 ≈ 0

## As a percentage:

^{120}/_{640,588} ≈ 0.02%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions