684/634 Simplified

Learn how to find what is 684/634 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 684/634 in simplest form.

To simplify 684/634 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 684/634 can be reduced in simplest form. In this case, the greatest common divisor of 684 and 634 is 2. Dividing both the numerator and denominator by GCD, the fraction 684/634 becomes 342/317 which is the simplest form.

Simplify 684/634 as a Fraction
Using Factorization:
684/634 = (?)
684/634 = (2 x 2 x 3 x 3 x 19)/(2 x 317)      //write 684/634 in terms of factors
= 342/317
684/634 = 342/317
684/634 simplified is 342/317

Using GCD:
684/634 = (?)
GCD of 684 and 634 is 2.
684/634 = (684/2)/(634/2)
= 342/317
684/634 = 342/317
684/634 simplified is 342/317 in fraction form
where,
684/634 is the given fraction to be simplified,
342/317 is the lowest term of 684/634.

Notes: Simplify 684/634 in lowest terms
1. 684/634 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 684 and 634 is 2 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 684/634 can be represented in its reduced form.
2. On the other hand, you can also reduce 684/634 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 684/634 becomes (2 x 2 x 3 x 3 x 19)/(2 x 317). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 684/634 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 684/634

what to be found:
684/634 = ?
Simplify 684/634 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 684/634.
Prime factors of 684 = 2 x 2 x 3 x 3 x 19

step 3 Find the prime factors of the denominator of given fraction 684/634.
Prime factors of 634 = 2 x 317

step 4 Rewrite the fraction 684/634 in the form of prime factors as like the below:
684/634= (2 x 2 x 3 x 3 x 19) / (2 x 317)

step 5 Check and reduce the factors of 684 and 634 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 3 x 19) / (2 x 317)
= ( 2 x 3 x 3 x 19)/( 317)
684/634 = 342/317

Hence,
684/634 in simplest form is 342/317.

Representing fraction 684/634 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 684/634 in its lowest terms.