384/464 Simplified

Learn how to find what is 384/464 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 384/464 in simplest form.

To simplify 384/464 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 384/464 can be reduced in simplest form. In this case, the greatest common divisor of 384 and 464 is 16. Dividing both the numerator and denominator by GCD, the fraction 384/464 becomes 24/29 which is the simplest form.

Simplify 384/464 as a Fraction
Using Factorization:
384/464 = (?)
384/464 = (2 x 2 x 2 x 2 x 2 x 2 x 2 x 3)/(2 x 2 x 2 x 2 x 29)      //write 384/464 in terms of factors
= 24/29
384/464 = 24/29
384/464 simplified is 24/29

Using GCD:
384/464 = (?)
GCD of 384 and 464 is 16.
384/464 = (384/16)/(464/16)
= 24/29
384/464 = 24/29
384/464 simplified is 24/29 in fraction form
where,
384/464 is the given fraction to be simplified,
24/29 is the lowest term of 384/464.

Notes: Simplify 384/464 in lowest terms
1. 384/464 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 384 and 464 is 16 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 384/464 can be represented in its reduced form.
2. On the other hand, you can also reduce 384/464 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 384/464 becomes (2 x 2 x 2 x 2 x 2 x 2 x 2 x 3)/(2 x 2 x 2 x 2 x 29). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 384/464 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 384/464

what to be found:
384/464 = ?
Simplify 384/464 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 384/464.
Prime factors of 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

step 3 Find the prime factors of the denominator of given fraction 384/464.
Prime factors of 464 = 2 x 2 x 2 x 2 x 29

step 4 Rewrite the fraction 384/464 in the form of prime factors as like the below:
384/464= (2 x 2 x 2 x 2 x 2 x 2 x 2 x 3) / (2 x 2 x 2 x 2 x 29)

step 5 Check and reduce the factors of 384 and 464 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 2 x 2 x 2 x 2 x 2 x 3) / (2 x 2 x 2 x 2 x 29)
= ( 2 x 2 x 2 x 3)/( 29)
384/464 = 24/29

Hence,
384/464 in simplest form is 24/29.

Representing fraction 384/464 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 384/464 in its lowest terms.