Use our free GCF of Fractions Calculator tool to compute the GCF of 398/682, 692/298 i.e 2/101618 easily. The following is the detailed procedure to determine the greatest common factor of fractions 398/682, 692/298.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 398/682,692/298
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 398/682,692/298, numerators are 398,692
Denominators are 682,298
The GCF of 398,692 is 2 .
LCM of 682,298 is 101618.
The greatest common factor of 398/682,692/298 = [GCF of 398,692]/[LCM of 682,298]= 2/101618
Therefore, the GCF of 398/682,692/298 is 2/101618.
To find the highest common factor of 398,692, we have to find the factors of both numbers and list the highest common factor.
The factors of 398 are 1, 2, 199, 398
The factors of 692 are 1, 2, 4, 173, 346, 692
The HCF of 398,692 is 2.
Lets's calculate GCF of 398,692
2 | 398, 692 |
199, 346 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 692
:1,2,4,173,346,692
Greatest Common Factor
We found the factors 398,692 . The biggest common factor number is the GCF number.
So the greatest common factor 398,692 is 2.
Lets's calculate LCM of 682,298
2 | 682, 298 |
341, 149 |
∴ So the LCM of the given numbers is 2 x 341 x 149 = 101618
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/101618
Therefore, the GCF of Fractions 398/682,692/298 is 2/101618
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 682,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(682,298) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(682,298) x common factors =2 x 1 = 2
LCM(682,298) = ( 682 × 298 ) / 2
LCM(682,298) = 203236 / 2
LCM(682,298) = 101618
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 398,692?
The HCF of 398,692 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 398/682, 692/298?
Answer: GCF of Numerators as per given numbers 398/682, 692/298 is
GCF of Numerators i.e. for 398,692 is 2
LCM of denominators i.e. for 682,298 is 101618.
Thus, GCF of Fractions is 2/101618.Finally, GCF of Fractions for 398/682, 692/298 is 2/101618.