685/65 Simplified

Learn how to find what is 685/65 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 685/65 in simplest form.

To reduce 685/65 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 685/65 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 685 and 65 is 5. Dividing both the numerator and denominator by GCF, the fraction 685/65 becomes 137/13 which is the simplest form.

685/65 Simplified as a Fraction
Using Factorization:
685/65 = (?)
685/65 = (5 x 137)/(5 x 13)      write 685/65 in terms of factors
= 137/13
685/65 = 137/13
685/65 simplified is 137/13

Using GCF
685/65 = (?)
GCF of 685 and 65 is 5.
685/65 = (685/5)/(65/5)
= 137/13
685/65 = 137/13
685/65 simplified is 137/13 in fraction form
where,
685/65 is the given fraction to be simplified,
137/13 is the lowest term of 685/65.

Notes: 685/65 simplified in lowest terms
1. 685/65 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 685 and 65 is 5 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 685/65 can be represented in its reduced form.
2. On the other hand, you can also reduce 685/65 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 685/65 becomes (5 x 137)/(5 x 13). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 685/65 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 685/65

what to be found:
685/65 = ?
Reduce 685/65 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 685/65.
Prime factors of 685 = 5 x 137

step 3 Find the prime factors of the denominator of given fraction 685/65.
Prime factors of 65 = 5 x 13

step 4 Rewrite the fraction 685/65 in the form of prime factors as like the below:
685/65= (5 x 137) / (5 x 13)

step 5 Check and reduce the factors of 685 and 65 if any factors in the numerator and denominator cancel each other:
= (5 x 137) / (5 x 13)
= ( 137)/( 13)
685/65 = 137/13
Hence,
685/65 in simplest form is 137/13.

685/65 simplified is 137/13, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 685/65 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 685/65 in its lowest terms.