138/378 Simplified

Learn how to find what is 138/378 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 138/378 in simplest form.

To simplify 138/378 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 138/378 can be reduced in simplest form. In this case, the greatest common divisor of 138 and 378 is 6. Dividing both the numerator and denominator by GCD, the fraction 138/378 becomes 23/63 which is the simplest form.

Simplify 138/378 as a Fraction
Using Factorization:
138/378 = (?)
138/378 = (2 x 3 x 23)/(2 x 3 x 3 x 3 x 7)      //write 138/378 in terms of factors
= 23/63
138/378 = 23/63
138/378 simplified is 23/63

Using GCD:
138/378 = (?)
GCD of 138 and 378 is 6.
138/378 = (138/6)/(378/6)
= 23/63
138/378 = 23/63
138/378 simplified is 23/63 in fraction form
where,
138/378 is the given fraction to be simplified,
23/63 is the lowest term of 138/378.

Notes: Simplify 138/378 in lowest terms
1. 138/378 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 138 and 378 is 6 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 138/378 can be represented in its reduced form.
2. On the other hand, you can also reduce 138/378 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 138/378 becomes (2 x 3 x 23)/(2 x 3 x 3 x 3 x 7). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 138/378 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 138/378

what to be found:
138/378 = ?
Simplify 138/378 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 138/378.
Prime factors of 138 = 2 x 3 x 23

step 3 Find the prime factors of the denominator of given fraction 138/378.
Prime factors of 378 = 2 x 3 x 3 x 3 x 7

step 4 Rewrite the fraction 138/378 in the form of prime factors as like the below:
138/378= (2 x 3 x 23) / (2 x 3 x 3 x 3 x 7)

step 5 Check and reduce the factors of 138 and 378 if any factors in the numerator and denominator cancel each other:
= (2 x 3 x 23) / (2 x 3 x 3 x 3 x 7)
= ( 23)/( 3 x 3 x 7)
138/378 = 23/63

Hence,
138/378 in simplest form is 23/63.

Representing fraction 138/378 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 138/378 in its lowest terms.