684/172 Simplified

Learn how to find what is 684/172 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 684/172 in simplest form.

To reduce 684/172 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 684/172 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 684 and 172 is 4. Dividing both the numerator and denominator by GCF, the fraction 684/172 becomes 171/43 which is the simplest form.

684/172 Simplified as a Fraction
Using Factorization:
684/172 = (?)
684/172 = (2 x 2 x 3 x 3 x 19)/(2 x 2 x 43)      write 684/172 in terms of factors
= 171/43
684/172 = 171/43
684/172 simplified is 171/43

Using GCF
684/172 = (?)
GCF of 684 and 172 is 4.
684/172 = (684/4)/(172/4)
= 171/43
684/172 = 171/43
684/172 simplified is 171/43 in fraction form
where,
684/172 is the given fraction to be simplified,
171/43 is the lowest term of 684/172.

Notes: 684/172 simplified in lowest terms
1. 684/172 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 684 and 172 is 4 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 684/172 can be represented in its reduced form.
2. On the other hand, you can also reduce 684/172 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 684/172 becomes (2 x 2 x 3 x 3 x 19)/(2 x 2 x 43). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 684/172 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 684/172

what to be found:
684/172 = ?
Reduce 684/172 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 684/172.
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 684/172.
Prime factors of 172 = 2 x 2 x 43

step 4 Rewrite the fraction 684/172 in the form of prime factors as like the below:
684/172= (2 x 2 x 3 x 3 x 19) / (2 x 2 x 43)

step 5 Check and reduce the factors of 684 and 172 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 3 x 19) / (2 x 2 x 43)
= ( 3 x 3 x 19)/( 43)
684/172 = 171/43
Hence,
684/172 in simplest form is 171/43.

684/172 simplified is 171/43, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 684/172 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 684/172 in its lowest terms.