Use our free GCF of Fractions Calculator tool to compute the GCF of 819/305, 838/185 i.e 1/11285 easily. The following is the detailed procedure to determine the greatest common factor of fractions 819/305, 838/185.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 819/305,838/185
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 819/305,838/185, numerators are 819,838
Denominators are 305,185
The GCF of 819,838 is 1 .
LCM of 305,185 is 11285.
The greatest common factor of 819/305,838/185 = [GCF of 819,838]/[LCM of 305,185]= 1/11285
Therefore, the GCF of 819/305,838/185 is 1/11285.
To find the highest common factor of 819,838, we have to find the factors of both numbers and list the highest common factor.
The factors of 819 are 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
The factors of 838 are 1, 2, 419, 838
The HCF of 819,838 is 1.
Lets's calculate GCF of 819,838
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 819
:1,3,7,9,13,21,39,63,91,117,273,819
Now, list down the factors of 838
:1,2,419,838
Greatest Common Factor
We found the factors 819,838 . The biggest common factor number is the GCF number.
So the greatest common factor 819,838 is 1.
Lets's calculate LCM of 305,185
5 | 305, 185 |
61, 37 |
∴ So the LCM of the given numbers is 5 x 61 x 37 = 11285
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11285
Therefore, the GCF of Fractions 819/305,838/185 is 1/11285
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 305,185 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,185) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(305,185) x common factors =5 x 1 = 5
LCM(305,185) = ( 305 × 185 ) / 5
LCM(305,185) = 56425 / 5
LCM(305,185) = 11285
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 819,838?
The HCF of 819,838 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 819/305, 838/185?
Answer: GCF of Numerators as per given numbers 819/305, 838/185 is
GCF of Numerators i.e. for 819,838 is 1
LCM of denominators i.e. for 305,185 is 11285.
Thus, GCF of Fractions is 1/11285.Finally, GCF of Fractions for 819/305, 838/185 is 1/11285.