Use our free GCF of Fractions Calculator tool to compute the GCF of 8114/473, 5478/1916 i.e 2/906268 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8114/473, 5478/1916.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8114/473,5478/1916
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 8114/473,5478/1916, numerators are 8114,5478
Denominators are 473,1916
The GCF of 8114,5478 is 2 .
LCM of 473,1916 is 906268.
The greatest common factor of 8114/473,5478/1916 = [GCF of 8114,5478]/[LCM of 473,1916]= 2/906268
Therefore, the GCF of 8114/473,5478/1916 is 2/906268.
To find the highest common factor of 8114,5478, we have to find the factors of both numbers and list the highest common factor.
The factors of 8114 are 1, 2, 4057, 8114
The factors of 5478 are 1, 2, 3, 6, 11, 22, 33, 66, 83, 166, 249, 498, 913, 1826, 2739, 5478
The HCF of 8114,5478 is 2.
Lets's calculate GCF of 8114,5478
2 | 8114, 5478 |
4057, 2739 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 8114
:1,2,4057,8114
Now, list down the factors of 5478
:1,2,3,6,11,22,33,66,83,166,249,498,913,1826,2739,5478
Greatest Common Factor
We found the factors 8114,5478 . The biggest common factor number is the GCF number.
So the greatest common factor 8114,5478 is 2.
Lets's calculate LCM of 473,1916
Given numbers has no common factors except 1. So, there LCM is their product i.e 906268
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/906268
Therefore, the GCF of Fractions 8114/473,5478/1916 is 2/906268
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 473,1916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(473,1916) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(473,1916) x common factors =1 x 1 = 1
LCM(473,1916) = ( 473 × 1916 ) / 1
LCM(473,1916) = 906268 / 1
LCM(473,1916) = 906268
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 8114,5478?
The HCF of 8114,5478 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 8114/473, 5478/1916?
Answer: GCF of Numerators as per given numbers 8114/473, 5478/1916 is
GCF of Numerators i.e. for 8114,5478 is 2
LCM of denominators i.e. for 473,1916 is 906268.
Thus, GCF of Fractions is 2/906268.Finally, GCF of Fractions for 8114/473, 5478/1916 is 2/906268.