What is 312/308 simplified as a fraction?
312/308 in simplest form is 78/77.
Learn how to find what is 312/308 simplified as a fraction just in a few minutes. We have covered why the GCF or factorization is important to simplify 312/308 in simplest form.
To reduce 312/308 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 312/308 can be reduced in simplest form. In this case, the (greatest common factor) GDF of 312 and 308 is 4. Dividing both the numerator and denominator by GCF, the fraction 312/308 becomes 78/77 which is the simplest form.
312/308 Simplified as a Fraction
Using Factorization:
312/308 = (?)
312/308 = (2 x 2 x 2 x 3 x 13)/(2 x 2 x 7 x 11) write 312/308 in terms of factors
= 78/77
312/308 = 78/77
312/308 simplified is 78/77
Using GCF
312/308 = (?)
GCF of 312 and 308 is 4.
312/308 = (312/4)/(308/4)
= 78/77
312/308 = 78/77
312/308 simplified is 78/77 in fraction form
where,
312/308 is the given fraction to be simplified,
78/77 is the lowest term of 312/308.
Notes: 312/308 simplified in lowest terms
1. 312/308 can be simplified only if the GCF of numerator and denominator is greater than 1. In this case, the GCF of 312 and 308 is 4 which is the greatest factor that evenly divides both numerator and denominator, so this fraction 312/308 can be represented in its reduced form.
2. On the other hand, you can also reduce 312/308 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 312/308 becomes (2 x 2 x 2 x 3 x 13)/(2 x 2 x 7 x 11). Now you can check and cancel the factors if any factors of numerator and denominator cancel each other to simplify 312/308 in its lowest terms.
step 1 Observe the input parameters and what to be found:
Input values:
Fraction = 312/308
what to be found:
312/308 = ?
Reduce 312/308 in lowest terms.
step 2 Find the prime factors of the numerator of given fraction 312/308.
Prime factors of 312 = 2 x 2 x 2 x 3 x 13
step 3 Find the prime factors of the denominator of given fraction 312/308.
Prime factors of 308 = 2 x 2 x 7 x 11
step 4 Rewrite the fraction 312/308 in the form of prime factors as like the below:
312/308= (2 x 2 x 2 x 3 x 13) / (2 x 2 x 7 x 11)
step 5 Check and reduce the factors of 312 and 308 if any factors in the numerator and denominator cancel each other:
= (2 x 2 x 2 x 3 x 13) / (2 x 2 x 7 x 11)
= ( 2 x 3 x 13)/( 7 x 11)
312/308 = 78/77
Hence,
312/308 in simplest form is 78/77.
312/308 simplified is 78/77, representing fraction in lowest terms is a better way than its original form, to easily recognize the fraction or use in mathematical operations. Simplifying 312/308 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 312/308 in its lowest terms.