Use our free GCF of Fractions Calculator tool to compute the GCF of 114/284, 3078/919 i.e 114/260996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 114/284, 3078/919.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 114/284,3078/919
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 114/284,3078/919, numerators are 114,3078
Denominators are 284,919
The GCF of 114,3078 is 114 .
LCM of 284,919 is 260996.
The greatest common factor of 114/284,3078/919 = [GCF of 114,3078]/[LCM of 284,919]= 114/260996
Therefore, the GCF of 114/284,3078/919 is 114/260996.
To find the highest common factor of 114,3078, we have to find the factors of both numbers and list the highest common factor.
The factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114
The factors of 3078 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078
The HCF of 114,3078 is 114.
Lets's calculate GCF of 114,3078
2 | 114, 3078 |
3 | 57, 1539 |
19 | 19, 513 |
1, 27 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Now, list down the factors of 114
:1,2,3,6,19,38,57,114
Now, list down the factors of 3078
:1,2,3,6,9,18,19,27,38,54,57,81,114,162,171,342,513,1026,1539,3078
Greatest Common Factor
We found the factors 114,3078 . The biggest common factor number is the GCF number.
So the greatest common factor 114,3078 is 114.
Lets's calculate LCM of 284,919
Given numbers has no common factors except 1. So, there LCM is their product i.e 260996
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/260996
Therefore, the GCF of Fractions 114/284,3078/919 is 114/260996
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 284,919 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(284,919) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(284,919) x common factors =1 x 1 = 1
LCM(284,919) = ( 284 × 919 ) / 1
LCM(284,919) = 260996 / 1
LCM(284,919) = 260996
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 114,3078?
The HCF of 114,3078 is 114
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 114/284, 3078/919?
Answer: GCF of Numerators as per given numbers 114/284, 3078/919 is
GCF of Numerators i.e. for 114,3078 is 114
LCM of denominators i.e. for 284,919 is 260996.
Thus, GCF of Fractions is 114/260996.Finally, GCF of Fractions for 114/284, 3078/919 is 114/260996.