117/208 Simplified

Learn how to find what is 117/208 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 117/208 in simplest form.

To simplify 117/208 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 117/208 can be reduced in simplest form. In this case, the greatest common divisor of 117 and 208 is 13. Dividing both the numerator and denominator by GCD, the fraction 117/208 becomes 9/16 which is the simplest form.

Simplify 117/208 as a Fraction
Using Factorization:
117/208 = (?)
117/208 = (3 x 3 x 13)/(2 x 2 x 2 x 2 x 13)      //write 117/208 in terms of factors
= 9/16
117/208 = 9/16
117/208 simplified is 9/16

Using GCD:
117/208 = (?)
GCD of 117 and 208 is 13.
117/208 = (117/13)/(208/13)
= 9/16
117/208 = 9/16
117/208 simplified is 9/16 in fraction form
where,
117/208 is the given fraction to be simplified,
9/16 is the lowest term of 117/208.

Notes: Simplify 117/208 in lowest terms
1. 117/208 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 117 and 208 is 13 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 117/208 can be represented in its reduced form.
2. On the other hand, you can also reduce 117/208 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 117/208 becomes (3 x 3 x 13)/(2 x 2 x 2 x 2 x 13). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 117/208 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 117/208

what to be found:
117/208 = ?
Simplify 117/208 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 117/208.
Prime factors of 117 = 3 x 3 x 13

step 3 Find the prime factors of the denominator of given fraction 117/208.
Prime factors of 208 = 2 x 2 x 2 x 2 x 13

step 4 Rewrite the fraction 117/208 in the form of prime factors as like the below:
117/208= (3 x 3 x 13) / (2 x 2 x 2 x 2 x 13)

step 5 Check and reduce the factors of 117 and 208 if any factors in the numerator and denominator cancel each other:
= (3 x 3 x 13) / (2 x 2 x 2 x 2 x 13)
= (3 x 3 )/(2 x 2 x 2 x 2 )
117/208 = 9/16

Hence,
117/208 in simplest form is 9/16.

Representing fraction 117/208 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 117/208 in its lowest terms.