Reduce (simplify) the fraction: 4,096/256
Detailed calculations below:
Fractions, brief introduction
A fraction consists of two numbers and the fraction bar: 4,096/256
The number above the fraction bar is the numerator: 4,096
The number under the fraction bar is the denominator: 256
The fraction bar means that the two numbers divide themselves:
4,096/256 = 4,096 ÷ 256
Divide the numerator by the denominator to get the value of the fraction:
The value = 4,096 ÷ 256
Percentages, short introduction
'Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% = p/100 = p ÷ 100
The fraction 100/100 = 100 ÷ 100 = 100% = 1
Multiply a number by the fraction 100/100,
... and its value will not change.
To completely reduce (simplify) a fraction to its lowest terms, divide the numerator and the denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd)
To calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd), we perform the prime factorization of the two numbers.
The prime factorization of the two numbers:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
4,096 = 212
4,096 is not a prime number but a composite one.
256 = 28
256 is not a prime number but a composite one.
* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.
Calculate the greatest (highest) common factor (divisor), gcf (hcf, gcd):
Multiply all the common prime factors, taken by their smallest exponents (powers).
gcf, hcf, gcd (4,096; 256) = 28 = 256
Divide the numerator and the denominator of the fraction by their greatest (highest) common factor (divisor), gcf (hcf, gcd).
(212 ÷ 28) / (28 ÷ 28) =
If the denominator of the fraction is 1, it can be omitted.
The fraction is now completely reduced (simplified) to its lowest terms.
A fraction that is completely reduced (simplified) to its lowest terms -- to its basic representation -- to its simplest form:
- is a fraction that can no longer be reduced,
- is a fraction with the smallest possible numerator and denominator.
A fully reduced fraction is called an irreducible fraction.
16 = 16/1 is an improper fraction.
An improper fraction: the numerator is greater than or equal to the denominator.
Rewrite the result. This continues below...
Rewrite the result.
As an improper fraction
(the denominator = 1):
16 = 16/1
As a percentage:
16 × 100/100 =
(16 × 100)/100 =
In other words:
1) Calculate the value of the fraction.
2) Multiply this number by 100.
3) Add the percent sign, %.
The final answer
This continues below...
The final answer:
:: Written in three ways ::
As an improper fraction:
4,096/256 = 16/1
As an integer:
4,096/256 = 16
As a percentage:
4,096/256 = 1,600%
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