108/40 Simplified

Learn how to find what is 108/40 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 108/40 in simplest form.

To simplify 108/40 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 108/40 can be reduced in simplest form. In this case, the greatest common divisor of 108 and 40 is 4. Dividing both the numerator and denominator by GCD, the fraction 108/40 becomes 27/10 which is the simplest form.

Simplify 108/40 as a Fraction
Using Factorization:
108/40 = (?)
108/40 = (2 x 2 x 3 x 3 x 3)/(2 x 2 x 2 x 5)      //write 108/40 in terms of factors
= 27/10
108/40 = 27/10
108/40 simplified is 27/10

Using GCD:
108/40 = (?)
GCD of 108 and 40 is 4.
108/40 = (108/4)/(40/4)
= 27/10
108/40 = 27/10
108/40 simplified is 27/10 in fraction form
where,
108/40 is the given fraction to be simplified,
27/10 is the lowest term of 108/40.

Notes: Simplify 108/40 in lowest terms
1. 108/40 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 108 and 40 is 4 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 108/40 can be represented in its reduced form.
2. On the other hand, you can also reduce 108/40 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 108/40 becomes (2 x 2 x 3 x 3 x 3)/(2 x 2 x 2 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 108/40 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 108/40

what to be found:
108/40 = ?
Simplify 108/40 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 108/40.
Prime factors of 108 = 2 x 2 x 3 x 3 x 3

step 3 Find the prime factors of the denominator of given fraction 108/40.
Prime factors of 40 = 2 x 2 x 2 x 5

step 4 Rewrite the fraction 108/40 in the form of prime factors as like the below:
108/40= (2 x 2 x 3 x 3 x 3) / (2 x 2 x 2 x 5)

step 5 Check and reduce the factors of 108 and 40 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 3 x 3) / (2 x 2 x 2 x 5)
= ( 3 x 3 x 3)/( 2 x 5)
108/40 = 27/10

Hence,
108/40 in simplest form is 27/10.

Representing fraction 108/40 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 108/40 in its lowest terms.