Use our free GCF of Fractions Calculator tool to compute the GCF of 614/193, 309/611 i.e 1/117923 easily. The following is the detailed procedure to determine the greatest common factor of fractions 614/193, 309/611.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 614/193,309/611
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 614/193,309/611, numerators are 614,309
Denominators are 193,611
The GCF of 614,309 is 1 .
LCM of 193,611 is 117923.
The greatest common factor of 614/193,309/611 = [GCF of 614,309]/[LCM of 193,611]= 1/117923
Therefore, the GCF of 614/193,309/611 is 1/117923.
To find the highest common factor of 614,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 614 are 1, 2, 307, 614
The factors of 309 are 1, 3, 103, 309
The HCF of 614,309 is 1.
Lets's calculate GCF of 614,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 614
:1,2,307,614
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 614,309 . The biggest common factor number is the GCF number.
So the greatest common factor 614,309 is 1.
Lets's calculate LCM of 193,611
Given numbers has no common factors except 1. So, there LCM is their product i.e 117923
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/117923
Therefore, the GCF of Fractions 614/193,309/611 is 1/117923
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 193,611 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(193,611) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(193,611) x common factors =1 x 1 = 1
LCM(193,611) = ( 193 × 611 ) / 1
LCM(193,611) = 117923 / 1
LCM(193,611) = 117923
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 614,309?
The HCF of 614,309 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 614/193, 309/611?
Answer: GCF of Numerators as per given numbers 614/193, 309/611 is
GCF of Numerators i.e. for 614,309 is 1
LCM of denominators i.e. for 193,611 is 117923.
Thus, GCF of Fractions is 1/117923.Finally, GCF of Fractions for 614/193, 309/611 is 1/117923.