## Reduce: ^{233,280,000}/_{8}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{233,280,000}/_{8}

#### The number above the bar is the numerator: 233,280,000

#### The number below the bar is the denominator: 8

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

^{233,280,000}/_{8} = 233,280,000 ÷ 8

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

Value = 233,280,000 ÷ 8

### 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.

#### 233,280,000 = 2^{9} × 3^{6} × 5^{4};

233,280,000 is not a prime, is a composite number;

#### 8 = 2^{3};

8 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 (233,280,000; 8) = 2^{3} = 8

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

^{233,280,000}/_{8} =

^{(29 × 36 × 54)}/_{23} =

^{((29 × 36 × 54) ÷ 23)} / _{(23 ÷ 23)} =

^{(26 × 36 × 54)}/_{1} =

^{29,160,000}/_{1} =

#### 29,160,000

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

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

### 29,160,000 = ^{29,160,000}/_{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):

#### 29,160,000 = ^{29,160,000}/_{1}

### As a percentage:

#### 29,160,000 =

#### 29,160,000 × ^{100}/_{100} =

^{(29,160,000 × 100)}/_{100} =

^{2,916,000,000}/_{100} =

#### 2,916,000,000%

#### 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...

## Final answer:

:: written in three ways ::

## As an improper fraction

(numerator larger than denominator):

^{233,280,000}/_{8} = ^{29,160,000}/_{1}

## As an integer:

^{233,280,000}/_{8} = 29,160,000

## As a percentage:

^{233,280,000}/_{8} = 2,916,000,000%

## More operations of this kind:

## Online calculator: reduce (simplify) fractions