Use our free GCF of Fractions Calculator tool to compute the GCF of 334/204, 993/310 i.e 1/31620 easily. The following is the detailed procedure to determine the greatest common factor of fractions 334/204, 993/310.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 334/204,993/310
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 334/204,993/310, numerators are 334,993
Denominators are 204,310
The GCF of 334,993 is 1 .
LCM of 204,310 is 31620.
The greatest common factor of 334/204,993/310 = [GCF of 334,993]/[LCM of 204,310]= 1/31620
Therefore, the GCF of 334/204,993/310 is 1/31620.
To find the highest common factor of 334,993, we have to find the factors of both numbers and list the highest common factor.
The factors of 334 are 1, 2, 167, 334
The factors of 993 are 1, 3, 331, 993
The HCF of 334,993 is 1.
Lets's calculate GCF of 334,993
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 334
:1,2,167,334
Now, list down the factors of 993
:1,3,331,993
Greatest Common Factor
We found the factors 334,993 . The biggest common factor number is the GCF number.
So the greatest common factor 334,993 is 1.
Lets's calculate LCM of 204,310
2 | 204, 310 |
102, 155 |
∴ So the LCM of the given numbers is 2 x 102 x 155 = 31620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31620
Therefore, the GCF of Fractions 334/204,993/310 is 1/31620
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 204,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,310) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(204,310) x common factors =2 x 1 = 2
LCM(204,310) = ( 204 × 310 ) / 2
LCM(204,310) = 63240 / 2
LCM(204,310) = 31620
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 334,993?
The HCF of 334,993 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 334/204, 993/310?
Answer: GCF of Numerators as per given numbers 334/204, 993/310 is
GCF of Numerators i.e. for 334,993 is 1
LCM of denominators i.e. for 204,310 is 31620.
Thus, GCF of Fractions is 1/31620.Finally, GCF of Fractions for 334/204, 993/310 is 1/31620.