686/500 Simplified

Learn how to find what is 686/500 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 686/500 in simplest form.

To reduce 686/500 in its lowest terms, you must be familiar with either how to find the greatest common factor or prime factors. Both of these methods are used to recognize if 686/500 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 686 and 500 is 2. Dividing both the numerator and denominator by GCF, the fraction 686/500 becomes 343/250 which is the simplest form.

686/500 Simplified as a Fraction
Using Factorization:
686/500 = (?)
686/500 = (2 x 7 x 7 x 7)/(2 x 2 x 5 x 5 x 5)      write 686/500 in terms of factors
= 343/250
686/500 = 343/250
686/500 simplified is 343/250

Using GCF
686/500 = (?)
GCF of 686 and 500 is 2.
686/500 = (686/2)/(500/2)
= 343/250
686/500 = 343/250
686/500 simplified is 343/250 in fraction form
where,
686/500 is the given fraction to be simplified,
343/250 is the lowest term of 686/500.

Notes: 686/500 simplified in lowest terms
1. 686/500 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 686 and 500 is 2 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 686/500 can be represented in its reduced form.
2. On the other hand, you can also reduce 686/500 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 686/500 becomes (2 x 7 x 7 x 7)/(2 x 2 x 5 x 5 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 686/500 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 686/500

what to be found:
686/500 = ?
Reduce 686/500 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 686/500.
Prime factors of 686 = 2 x 7 x 7 x 7

step 3 Find the prime factors of the denominator of given fraction 686/500.
Prime factors of 500 = 2 x 2 x 5 x 5 x 5

step 4 Rewrite the fraction 686/500 in the form of prime factors as like the below:
686/500= (2 x 7 x 7 x 7) / (2 x 2 x 5 x 5 x 5)

step 5 Check and reduce the factors of 686 and 500 if any factors in the numerator and denominator cancel each other:
= (2 x 7 x 7 x 7) / (2 x 2 x 5 x 5 x 5)
= ( 7 x 7 x 7)/( 2 x 5 x 5 x 5)
686/500 = 343/250
Hence,
686/500 in simplest form is 343/250.

686/500 simplified is 343/250, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 686/500 to its simplest form involves the greatest common factor or factorization. Recognizing the GCF or prime factors of numerator and denominator of a fraction is key when you start reducing fractions like 686/500 in its lowest terms.