748/30 Simplified

Learn how to find what is 748/30 simplified as a fraction just in a few minutes. We have covered why the greatest common divisor or factorization is important to simplify 748/30 in simplest form.

To simplify 748/30 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 748/30 can be reduced in simplest form. In this case, the greatest common divisor of 748 and 30 is 2. Dividing both the numerator and denominator by GCD, the fraction 748/30 becomes 374/15 which is the simplest form.

Simplify 748/30 as a Fraction
Using Factorization:
748/30 = (?)
748/30 = (2 x 2 x 11 x 17)/(2 x 3 x 5)      //write 748/30 in terms of factors
= 374/15
748/30 = 374/15
748/30 simplified is 374/15

Using GCD:
748/30 = (?)
GCD of 748 and 30 is 2.
748/30 = (748/2)/(30/2)
= 374/15
748/30 = 374/15
748/30 simplified is 374/15 in fraction form
where,
748/30 is the given fraction to be simplified,
374/15 is the lowest term of 748/30.

Notes: Simplify 748/30 in lowest terms
1. 748/30 can be simplified only if the GCD of numerator and denominator is greater than 1. In this case, the GCD of 748 and 30 is 2 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 748/30 can be represented in its reduced form.
2. On the other hand, you can also reduce 748/30 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 748/30 becomes (2 x 2 x 11 x 17)/(2 x 3 x 5). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 748/30 in its lowest terms.

step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 748/30

what to be found:
748/30 = ?
Simplify 748/30 in lowest terms.

step 2 Find the prime factors of the numerator of given fraction 748/30.
Prime factors of 748 = 2 x 2 x 11 x 17

step 3 Find the prime factors of the denominator of given fraction 748/30.
Prime factors of 30 = 2 x 3 x 5

step 4 Rewrite the fraction 748/30 in the form of prime factors as like the below:
748/30= (2 x 2 x 11 x 17) / (2 x 3 x 5)

step 5 Check and reduce the factors of 748 and 30 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 11 x 17) / (2 x 3 x 5)
= ( 2 x 11 x 17)/( 3 x 5)
748/30 = 374/15

Hence,
748/30 in simplest form is 374/15.

Representing fraction 748/30 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 748/30 in its lowest terms.