49/420 Simplified

Learn how to find what is 49/420 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 49/420 in simplest form.

To simplify 49/420 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 49/420 can be reduced in simplest form. In this case, the greatest common divisor of 49 and 420 is 7. Dividing both the numerator and denominator by GCD, the fraction 49/420 becomes 7/60 which is the simplest form.

Simplify 49/420 as a Fraction
Using Factorization:
49/420 = (?)
49/420 = (7 x 7)/(2 x 2 x 3 x 5 x 7)      //write 49/420 in terms of factors
= 7/60
49/420 = 7/60
49/420 simplified is 7/60

Using GCD:
49/420 = (?)
GCD of 49 and 420 is 7.
49/420 = (49/7)/(420/7)
= 7/60
49/420 = 7/60
49/420 simplified is 7/60 in fraction form
where,
49/420 is the given fraction to be simplified,
7/60 is the lowest term of 49/420.

Notes: Simplify 49/420 in lowest terms
1. 49/420 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 49 and 420 is 7 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 49/420 can be represented in its reduced form.
2. On the other hand, you can also reduce 49/420 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 49/420 becomes (7 x 7)/(2 x 2 x 3 x 5 x 7). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 49/420 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 49/420

what to be found:
49/420 = ?
Simplify 49/420 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 49/420.
Prime factors of 49 = 7 x 7

step 3 Find the prime factors of the denominator of given fraction 49/420.
Prime factors of 420 = 2 x 2 x 3 x 5 x 7

step 4 Rewrite the fraction 49/420 in the form of prime factors as like the below:
49/420= (7 x 7) / (2 x 2 x 3 x 5 x 7)

step 5 Check and reduce the factors of 49 and 420 if any factors in the numerator and denominator cancel each other:
= (7 x 7) / (2 x 2 x 3 x 5 x 7)
= ( 7)/(2 x 2 x 3 x 5 )
49/420 = 7/60

Hence,
49/420 in simplest form is 7/60.

Representing fraction 49/420 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 49/420 in its lowest terms.