310/180 Simplified

Learn how to find what is 310/180 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 310/180 in simplest form.

To simplify 310/180 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 310/180 can be reduced in simplest form. In this case, the greatest common divisor of 310 and 180 is 10. Dividing both the numerator and denominator by GCD, the fraction 310/180 becomes 31/18 which is the simplest form.

Simplify 310/180 as a Fraction
Using Factorization:
310/180 = (?)
310/180 = (2 x 5 x 31)/(2 x 2 x 3 x 3 x 5)      //write 310/180 in terms of factors
= 31/18
310/180 = 31/18
310/180 simplified is 31/18

Using GCD:
310/180 = (?)
GCD of 310 and 180 is 10.
310/180 = (310/10)/(180/10)
= 31/18
310/180 = 31/18
310/180 simplified is 31/18 in fraction form
where,
310/180 is the given fraction to be simplified,
31/18 is the lowest term of 310/180.

Notes: Simplify 310/180 in lowest terms
1. 310/180 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 310 and 180 is 10 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 310/180 can be represented in its reduced form.
2. On the other hand, you can also reduce 310/180 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 310/180 becomes (2 x 5 x 31)/(2 x 2 x 3 x 3 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 310/180 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 310/180

what to be found:
310/180 = ?
Simplify 310/180 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 310/180.
Prime factors of 310 = 2 x 5 x 31

step 3 Find the prime factors of the denominator of given fraction 310/180.
Prime factors of 180 = 2 x 2 x 3 x 3 x 5

step 4 Rewrite the fraction 310/180 in the form of prime factors as like the below:
310/180= (2 x 5 x 31) / (2 x 2 x 3 x 3 x 5)

step 5 Check and reduce the factors of 310 and 180 if any factors in the numerator and denominator cancel each other:
= (2 x 5 x 31) / (2 x 2 x 3 x 3 x 5)
= ( 31)/( 2 x 3 x 3 )
310/180 = 31/18

Hence,
310/180 in simplest form is 31/18.

Representing fraction 310/180 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 310/180 in its lowest terms.