## Reduce: ^{180,102,363}/_{257,289,084}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{180,102,363}/_{257,289,084}

#### The number above the bar is the numerator: 180,102,363

#### The number below the bar is the denominator: 257,289,084

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

^{180,102,363}/_{257,289,084} = 180,102,363 ÷ 257,289,084

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

Value = 180,102,363 ÷ 257,289,084

### 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.

#### 180,102,363 = 3 × 7 × 71 × 199 × 607;

180,102,363 is not a prime, is a composite number;

#### 257,289,084 = 2^{2} × 3^{2} × 13 × 17 × 73 × 443;

257,289,084 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 (180,102,363; 257,289,084) = 3

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

^{180,102,363}/_{257,289,084} =

^{(3 × 7 × 71 × 199 × 607)}/_{(22 × 32 × 13 × 17 × 73 × 443)} =

^{((3 × 7 × 71 × 199 × 607) ÷ 3)} / _{((22 × 32 × 13 × 17 × 73 × 443) ÷ 3)} =

^{(7 × 71 × 199 × 607)}/_{(22 × 3 × 13 × 17 × 73 × 443)} =

^{60,034,121}/_{85,763,028}

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

^{60,034,121}/_{85,763,028} 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:

^{60,034,121}/_{85,763,028} =

#### 60,034,121 ÷ 85,763,028 ≈

#### 0.700000016324 ≈

#### 0.7

### As a percentage:

#### 0.700000016324 =

#### 0.700000016324 × ^{100}/_{100} =

#### ^{70.000001632405}/_{100} =

#### 70.000001632405% ≈

#### 70%

#### 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):

^{180,102,363}/_{257,289,084} = ^{60,034,121}/_{85,763,028}

## As a decimal number:

^{180,102,363}/_{257,289,084} ≈ 0.700000016324 ≈ 0.7

## As a percentage:

^{180,102,363}/_{257,289,084} ≈ 70%

## More operations of this kind:

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