130/420 Simplified

Learn how to find what is 130/420 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 130/420 in simplest form.

To reduce 130/420 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 130/420 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 130 and 420 is 10. Dividing both the numerator and denominator by GCF, the fraction 130/420 becomes 13/42 which is the simplest form.

130/420 Simplified as a Fraction
Using Factorization:
130/420 = (?)
130/420 = (2 x 5 x 13)/(2 x 2 x 3 x 5 x 7)      write 130/420 in terms of factors
= 13/42
130/420 = 13/42
130/420 simplified is 13/42

Using GCF
130/420 = (?)
GCF of 130 and 420 is 10.
130/420 = (130/10)/(420/10)
= 13/42
130/420 = 13/42
130/420 simplified is 13/42 in fraction form
where,
130/420 is the given fraction to be simplified,
13/42 is the lowest term of 130/420.

Notes: 130/420 simplified in lowest terms
1. 130/420 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 130 and 420 is 10 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 130/420 can be represented in its reduced form.
2. On the other hand, you can also reduce 130/420 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 130/420 becomes (2 x 5 x 13)/(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 130/420 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 130/420

what to be found:
130/420 = ?
Reduce 130/420 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 130/420.
Prime factors of 130 = 2 x 5 x 13

step 3 Find the prime factors of the denominator of given fraction 130/420.
Prime factors of 420 = 2 x 2 x 3 x 5 x 7

step 4 Rewrite the fraction 130/420 in the form of prime factors as like the below:
130/420= (2 x 5 x 13) / (2 x 2 x 3 x 5 x 7)

step 5 Check and reduce the factors of 130 and 420 if any factors in the numerator and denominator cancel each other:
= (2 x 5 x 13) / (2 x 2 x 3 x 5 x 7)
= ( 13)/( 2 x 3 x 7)
130/420 = 13/42
Hence,
130/420 in simplest form is 13/42.

130/420 simplified is 13/42, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 130/420 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 130/420 in its lowest terms.