317520/362880 Simplified

Learn how to find what is 317520/362880 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 317520/362880 in simplest form.

To simplify 317520/362880 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 317520/362880 can be reduced in simplest form. In this case, the greatest common divisor of 317520 and 362880 is 45360. Dividing both the numerator and denominator by GCD, the fraction 317520/362880 becomes 7/8 which is the simplest form.

Simplify 317520/362880 as a Fraction
Using Factorization:
317520/362880 = (?)
317520/362880 = (2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 7)/(2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7)      //write 317520/362880 in terms of factors
= 7/8
317520/362880 = 7/8
317520/362880 simplified is 7/8

Using GCD:
317520/362880 = (?)
GCD of 317520 and 362880 is 45360.
317520/362880 = (317520/45360)/(362880/45360)
= 7/8
317520/362880 = 7/8
317520/362880 simplified is 7/8 in fraction form
where,
317520/362880 is the given fraction to be simplified,
7/8 is the lowest term of 317520/362880.

Notes: Simplify 317520/362880 in lowest terms
1. 317520/362880 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 317520 and 362880 is 45360 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 317520/362880 can be represented in its reduced form.
2. On the other hand, you can also reduce 317520/362880 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 317520/362880 becomes (2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 7)/(2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 317520/362880 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 317520/362880

what to be found:
317520/362880 = ?
Simplify 317520/362880 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 317520/362880.
Prime factors of 317520 = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 7

step 3 Find the prime factors of the denominator of given fraction 317520/362880.
Prime factors of 362880 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7

step 4 Rewrite the fraction 317520/362880 in the form of prime factors as like the below:
317520/362880= (2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 7) / (2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7)

step 5 Check and reduce the factors of 317520 and 362880 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 7) / (2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7)
= ( 7)/( 2 x 2 x 2 )
317520/362880 = 7/8

Hence,
317520/362880 in simplest form is 7/8.

Representing fraction 317520/362880 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 317520/362880 in its lowest terms.