564/480 Simplified

Learn how to find what is 564/480 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 564/480 in simplest form.

To simplify 564/480 in its lowest terms, you must be familiar with either how to find the greatest common divisor or prime factors. Both of these methods are used to recognize if 564/480 can be reduced in simplest form. In this case, the greatest common divisor of 564 and 480 is 12. Dividing both the numerator and denominator by GCD, the fraction 564/480 becomes 47/40 which is the simplest form.

Simplify 564/480 as a Fraction
Using Factorization:
564/480 = (?)
564/480 = (2 x 2 x 3 x 47)/(2 x 2 x 2 x 2 x 2 x 3 x 5)      //write 564/480 in terms of factors
= 47/40
564/480 = 47/40
564/480 simplified is 47/40

Using GCD:
564/480 = (?)
GCD of 564 and 480 is 12.
564/480 = (564/12)/(480/12)
= 47/40
564/480 = 47/40
564/480 simplified is 47/40 in fraction form
where,
564/480 is the given fraction to be simplified,
47/40 is the lowest term of 564/480.

Notes: Simplify 564/480 in lowest terms
1. 564/480 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 564 and 480 is 12 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 564/480 can be represented in its reduced form.
2. On the other hand, you can also reduce 564/480 in simplest form by using the factorization method. In this case, the numerator and denominator of fraction should be written in the form of prime factors, so the fraction 564/480 becomes (2 x 2 x 3 x 47)/(2 x 2 x 2 x 2 x 2 x 3 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 564/480 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 564/480

what to be found:
564/480 = ?
Simplify 564/480 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 564/480.
Prime factors of 564 = 2 x 2 x 3 x 47

step 3 Find the prime factors of the denominator of given fraction 564/480.
Prime factors of 480 = 2 x 2 x 2 x 2 x 2 x 3 x 5

step 4 Rewrite the fraction 564/480 in the form of prime factors as like the below:
564/480= (2 x 2 x 3 x 47) / (2 x 2 x 2 x 2 x 2 x 3 x 5)

step 5 Check and reduce the factors of 564 and 480 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 47) / (2 x 2 x 2 x 2 x 2 x 3 x 5)
= ( 47)/( 2 x 2 x 2 x 5)
564/480 = 47/40

Hence,
564/480 in simplest form is 47/40.

Representing fraction 564/480 in lowest terms is a better way than its original form to easily recognize the fraction or use in mathematical operations. Simplify fraction involves finding the greatest common factor or factorization. Recognizing the GCD or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 564/480 in its lowest terms.