420/108 Simplified

Learn how to find what is 420/108 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 420/108 in simplest form.

To simplify 420/108 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 420/108 can be reduced in simplest form. In this case, the greatest common divisor of 420 and 108 is 12. Dividing both the numerator and denominator by GCD, the fraction 420/108 becomes 35/9 which is the simplest form.

Simplify 420/108 as a Fraction
Using Factorization:
420/108 = (?)
420/108 = (2 x 2 x 3 x 5 x 7)/(2 x 2 x 3 x 3 x 3)      //write 420/108 in terms of factors
= 35/9
420/108 = 35/9
420/108 simplified is 35/9

Using GCD:
420/108 = (?)
GCD of 420 and 108 is 12.
420/108 = (420/12)/(108/12)
= 35/9
420/108 = 35/9
420/108 simplified is 35/9 in fraction form
where,
420/108 is the given fraction to be simplified,
35/9 is the lowest term of 420/108.

Notes: Simplify 420/108 in lowest terms
1. 420/108 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 420 and 108 is 12 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 420/108 can be represented in its reduced form.
2. On the other hand, you can also reduce 420/108 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 420/108 becomes (2 x 2 x 3 x 5 x 7)/(2 x 2 x 3 x 3 x 3). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 420/108 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 420/108

what to be found:
420/108 = ?
Simplify 420/108 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 420/108.
Prime factors of 420 = 2 x 2 x 3 x 5 x 7

step 3 Find the prime factors of the denominator of given fraction 420/108.
Prime factors of 108 = 2 x 2 x 3 x 3 x 3

step 4 Rewrite the fraction 420/108 in the form of prime factors as like the below:
420/108= (2 x 2 x 3 x 5 x 7) / (2 x 2 x 3 x 3 x 3)

step 5 Check and reduce the factors of 420 and 108 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 3 x 5 x 7) / (2 x 2 x 3 x 3 x 3)
= ( 5 x 7)/( 3 x 3)
420/108 = 35/9

Hence,
420/108 in simplest form is 35/9.

Representing fraction 420/108 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 420/108 in its lowest terms.