Use our free GCF of Fractions Calculator tool to compute the GCF of 378/419, 260/238 i.e 2/99722 easily. The following is the detailed procedure to determine the greatest common factor of fractions 378/419, 260/238.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 378/419,260/238
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 378/419,260/238, numerators are 378,260
Denominators are 419,238
The GCF of 378,260 is 2 .
LCM of 419,238 is 99722.
The greatest common factor of 378/419,260/238 = [GCF of 378,260]/[LCM of 419,238]= 2/99722
Therefore, the GCF of 378/419,260/238 is 2/99722.
To find the highest common factor of 378,260, 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 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
The HCF of 378,260 is 2.
Lets's calculate GCF of 378,260
2 | 378, 260 |
189, 130 |
∴ So the GCF of the given numbers is 2 = 2
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 260
:1,2,4,5,10,13,20,26,52,65,130,260
Greatest Common Factor
We found the factors 378,260 . The biggest common factor number is the GCF number.
So the greatest common factor 378,260 is 2.
Lets's calculate LCM of 419,238
Given numbers has no common factors except 1. So, there LCM is their product i.e 99722
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/99722
Therefore, the GCF of Fractions 378/419,260/238 is 2/99722
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 419,238 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,238) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,238) x common factors =1 x 1 = 1
LCM(419,238) = ( 419 × 238 ) / 1
LCM(419,238) = 99722 / 1
LCM(419,238) = 99722
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 378,260?
The HCF of 378,260 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 378/419, 260/238?
Answer: GCF of Numerators as per given numbers 378/419, 260/238 is
GCF of Numerators i.e. for 378,260 is 2
LCM of denominators i.e. for 419,238 is 99722.
Thus, GCF of Fractions is 2/99722.Finally, GCF of Fractions for 378/419, 260/238 is 2/99722.