Use our free GCF of Fractions Calculator tool to compute the GCF of 798/984, 114/873 i.e 114/286344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 798/984, 114/873.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 798/984,114/873
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 798/984,114/873, numerators are 798,114
Denominators are 984,873
The GCF of 798,114 is 114 .
LCM of 984,873 is 286344.
The greatest common factor of 798/984,114/873 = [GCF of 798,114]/[LCM of 984,873]= 114/286344
Therefore, the GCF of 798/984,114/873 is 114/286344.
To find the highest common factor of 798,114, we have to find the factors of both numbers and list the highest common factor.
The factors of 798 are 1, 2, 3, 6, 7, 14, 19, 21, 38, 42, 57, 114, 133, 266, 399, 798
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The HCF of 798,114 is 114.
Lets's calculate GCF of 798,114
2 | 798, 114 |
3 | 399, 57 |
19 | 133, 19 |
7, 1 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Now, list down the factors of 798
:1,2,3,6,7,14,19,21,38,42,57,114,133,266,399,798
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors 798,114 . The biggest common factor number is the GCF number.
So the greatest common factor 798,114 is 114.
Lets's calculate LCM of 984,873
3 | 984, 873 |
328, 291 |
∴ So the LCM of the given numbers is 3 x 328 x 291 = 286344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/286344
Therefore, the GCF of Fractions 798/984,114/873 is 114/286344
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 984,873 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(984,873) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(984,873) x common factors =3 x 1 = 3
LCM(984,873) = ( 984 × 873 ) / 3
LCM(984,873) = 859032 / 3
LCM(984,873) = 286344
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 798,114?
The HCF of 798,114 is 114
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 798/984, 114/873?
Answer: GCF of Numerators as per given numbers 798/984, 114/873 is
GCF of Numerators i.e. for 798,114 is 114
LCM of denominators i.e. for 984,873 is 286344.
Thus, GCF of Fractions is 114/286344.Finally, GCF of Fractions for 798/984, 114/873 is 114/286344.