Use our free GCF of Fractions Calculator tool to compute the GCF of 6921/213, 8766/138 i.e 9/9798 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6921/213, 8766/138.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6921/213,8766/138
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 6921/213,8766/138, numerators are 6921,8766
Denominators are 213,138
The GCF of 6921,8766 is 9 .
LCM of 213,138 is 9798.
The greatest common factor of 6921/213,8766/138 = [GCF of 6921,8766]/[LCM of 213,138]= 9/9798
Therefore, the GCF of 6921/213,8766/138 is 9/9798.
To find the highest common factor of 6921,8766, we have to find the factors of both numbers and list the highest common factor.
The factors of 6921 are 1, 3, 9, 769, 2307, 6921
The factors of 8766 are 1, 2, 3, 6, 9, 18, 487, 974, 1461, 2922, 4383, 8766
The HCF of 6921,8766 is 9.
Lets's calculate GCF of 6921,8766
3 | 6921, 8766 |
3 | 2307, 2922 |
769, 974 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 6921
:1,3,9,769,2307,6921
Now, list down the factors of 8766
:1,2,3,6,9,18,487,974,1461,2922,4383,8766
Greatest Common Factor
We found the factors 6921,8766 . The biggest common factor number is the GCF number.
So the greatest common factor 6921,8766 is 9.
Lets's calculate LCM of 213,138
3 | 213, 138 |
71, 46 |
∴ So the LCM of the given numbers is 3 x 71 x 46 = 9798
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/9798
Therefore, the GCF of Fractions 6921/213,8766/138 is 9/9798
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 213,138 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,138) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(213,138) x common factors =3 x 1 = 3
LCM(213,138) = ( 213 × 138 ) / 3
LCM(213,138) = 29394 / 3
LCM(213,138) = 9798
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 6921,8766?
The HCF of 6921,8766 is 9
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 6921/213, 8766/138?
Answer: GCF of Numerators as per given numbers 6921/213, 8766/138 is
GCF of Numerators i.e. for 6921,8766 is 9
LCM of denominators i.e. for 213,138 is 9798.
Thus, GCF of Fractions is 9/9798.Finally, GCF of Fractions for 6921/213, 8766/138 is 9/9798.