Use our free GCF of Fractions Calculator tool to compute the GCF of 654/204, 298/434 i.e 2/44268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/204, 298/434.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 654/204,298/434
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 654/204,298/434, numerators are 654,298
Denominators are 204,434
The GCF of 654,298 is 2 .
LCM of 204,434 is 44268.
The greatest common factor of 654/204,298/434 = [GCF of 654,298]/[LCM of 204,434]= 2/44268
Therefore, the GCF of 654/204,298/434 is 2/44268.
To find the highest common factor of 654,298, we have to find the factors of both numbers and list the highest common factor.
The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654
The factors of 298 are 1, 2, 149, 298
The HCF of 654,298 is 2.
Lets's calculate GCF of 654,298
2 | 654, 298 |
327, 149 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 654
:1,2,3,6,109,218,327,654
Now, list down the factors of 298
:1,2,149,298
Greatest Common Factor
We found the factors 654,298 . The biggest common factor number is the GCF number.
So the greatest common factor 654,298 is 2.
Lets's calculate LCM of 204,434
2 | 204, 434 |
102, 217 |
∴ So the LCM of the given numbers is 2 x 102 x 217 = 44268
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/44268
Therefore, the GCF of Fractions 654/204,298/434 is 2/44268
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 204,434 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,434) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(204,434) x common factors =2 x 1 = 2
LCM(204,434) = ( 204 × 434 ) / 2
LCM(204,434) = 88536 / 2
LCM(204,434) = 44268
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 654,298?
The HCF of 654,298 is 2
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 654/204, 298/434?
Answer: GCF of Numerators as per given numbers 654/204, 298/434 is
GCF of Numerators i.e. for 654,298 is 2
LCM of denominators i.e. for 204,434 is 44268.
Thus, GCF of Fractions is 2/44268.Finally, GCF of Fractions for 654/204, 298/434 is 2/44268.