Use our free GCF of Fractions Calculator tool to compute the GCF of 378/684, 135/678 i.e 27/77292 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/684, 135/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 378/684,135/678
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 378/684,135/678, numerators are 378,135
Denominators are 684,678
The GCF of 378,135 is 27 .
LCM of 684,678 is 77292.
The greatest common factor of 378/684,135/678 = [GCF of 378,135]/[LCM of 684,678]= 27/77292
Therefore, the GCF of 378/684,135/678 is 27/77292.
To find the highest common factor of 378,135, we have to find the factors of both numbers and list the highest common factor.
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The HCF of 378,135 is 27.
Lets's calculate GCF of 378,135
3 | 378, 135 |
3 | 126, 45 |
3 | 42, 15 |
14, 5 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Now, list down the factors of 135
:1,3,5,9,15,27,45,135
Greatest Common Factor
We found the factors 378,135 . The biggest common factor number is the GCF number.
So the greatest common factor 378,135 is 27.
Lets's calculate LCM of 684,678
2 | 684, 678 |
3 | 342, 339 |
114, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 114 x 113 = 77292
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/77292
Therefore, the GCF of Fractions 378/684,135/678 is 27/77292
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 684,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,678) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(684,678) x common factors =6 x 1 = 6
LCM(684,678) = ( 684 × 678 ) / 6
LCM(684,678) = 463752 / 6
LCM(684,678) = 77292
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 378,135?
The HCF of 378,135 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 378/684, 135/678?
Answer: GCF of Numerators as per given numbers 378/684, 135/678 is
GCF of Numerators i.e. for 378,135 is 27
LCM of denominators i.e. for 684,678 is 77292.
Thus, GCF of Fractions is 27/77292.Finally, GCF of Fractions for 378/684, 135/678 is 27/77292.