## Reduce: ^{24,465}/_{855,114,624}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{24,465}/_{855,114,624}

#### The number above the bar is the numerator: 24,465

#### The number below the bar is the denominator: 855,114,624

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

^{24,465}/_{855,114,624} = 24,465 ÷ 855,114,624

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

Value = 24,465 ÷ 855,114,624

### 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.

#### 24,465 = 3 × 5 × 7 × 233;

24,465 is not a prime, is a composite number;

#### 855,114,624 = 2^{7} × 3^{3} × 7 × 13 × 2,719;

855,114,624 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 (24,465; 855,114,624) = 3 × 7 = 21

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

^{24,465}/_{855,114,624} =

^{(3 × 5 × 7 × 233)}/_{(27 × 33 × 7 × 13 × 2,719)} =

^{((3 × 5 × 7 × 233) ÷ (3 × 7))} / _{((27 × 33 × 7 × 13 × 2,719) ÷ (3 × 7))} =

^{(5 × 233)}/_{(27 × 32 × 13 × 2,719)} =

^{1,165}/_{40,719,744}

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

^{1,165}/_{40,719,744} 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:

^{1,165}/_{40,719,744} =

#### 1,165 ÷ 40,719,744 ≈

#### 0.0000286102 ≈

#### 0

### As a percentage:

#### 0.0000286102 =

#### 0.0000286102 × ^{100}/_{100} =

#### ^{0.002861019951}/_{100} =

#### 0.002861019951% ≈

#### 0%

#### 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):

^{24,465}/_{855,114,624} = ^{1,165}/_{40,719,744}

## As a decimal number:

^{24,465}/_{855,114,624} ≈ 0.0000286102 ≈ 0

## As a percentage:

^{24,465}/_{855,114,624} ≈ 0%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions