Use our free GCF of Fractions Calculator tool to compute the GCF of 135/618, 108/721 i.e 27/4326 easily. The following is the detailed procedure to determine the greatest common factor of fractions 135/618, 108/721.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 135/618,108/721
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 135/618,108/721, numerators are 135,108
Denominators are 618,721
The GCF of 135,108 is 27 .
LCM of 618,721 is 4326.
The greatest common factor of 135/618,108/721 = [GCF of 135,108]/[LCM of 618,721]= 27/4326
Therefore, the GCF of 135/618,108/721 is 27/4326.
To find the highest common factor of 135,108, we have to find the factors of both numbers and list the highest common factor.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The HCF of 135,108 is 27.
Lets's calculate GCF of 135,108
3 | 135, 108 |
3 | 45, 36 |
3 | 15, 12 |
5, 4 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 135
:1,3,5,9,15,27,45,135
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Greatest Common Factor
We found the factors 135,108 . The biggest common factor number is the GCF number.
So the greatest common factor 135,108 is 27.
Lets's calculate LCM of 618,721
103 | 618, 721 |
6, 7 |
∴ So the LCM of the given numbers is 103 x 6 x 7 = 4326
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/4326
Therefore, the GCF of Fractions 135/618,108/721 is 27/4326
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 618,721 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(618,721) = 103
common factors(in case of two or more numbers have common factors) = 1
GCF(618,721) x common factors =103 x 1 = 103
LCM(618,721) = ( 618 × 721 ) / 103
LCM(618,721) = 445578 / 103
LCM(618,721) = 4326
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 135,108?
The HCF of 135,108 is 27
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 135/618, 108/721?
Answer: GCF of Numerators as per given numbers 135/618, 108/721 is
GCF of Numerators i.e. for 135,108 is 27
LCM of denominators i.e. for 618,721 is 4326.
Thus, GCF of Fractions is 27/4326.Finally, GCF of Fractions for 135/618, 108/721 is 27/4326.