Use our free GCF of Fractions Calculator tool to compute the GCF of 112/834, 196/284 i.e 28/118428 easily. The following is the detailed procedure to determine the greatest common factor of fractions 112/834, 196/284.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 112/834,196/284
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 112/834,196/284, numerators are 112,196
Denominators are 834,284
The GCF of 112,196 is 28 .
LCM of 834,284 is 118428.
The greatest common factor of 112/834,196/284 = [GCF of 112,196]/[LCM of 834,284]= 28/118428
Therefore, the GCF of 112/834,196/284 is 28/118428.
To find the highest common factor of 112,196, we have to find the factors of both numbers and list the highest common factor.
The factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196
The HCF of 112,196 is 28.
Lets's calculate GCF of 112,196
2 | 112, 196 |
2 | 56, 98 |
7 | 28, 49 |
4, 7 |
∴ So the GCF of the given numbers is 2 x 2 x 7 = 28
Now, list down the factors of 112
:1,2,4,7,8,14,16,28,56,112
Now, list down the factors of 196
:1,2,4,7,14,28,49,98,196
Greatest Common Factor
We found the factors 112,196 . The biggest common factor number is the GCF number.
So the greatest common factor 112,196 is 28.
Lets's calculate LCM of 834,284
2 | 834, 284 |
417, 142 |
∴ So the LCM of the given numbers is 2 x 417 x 142 = 118428
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 28/118428
Therefore, the GCF of Fractions 112/834,196/284 is 28/118428
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 834,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(834,284) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(834,284) x common factors =2 x 1 = 2
LCM(834,284) = ( 834 × 284 ) / 2
LCM(834,284) = 236856 / 2
LCM(834,284) = 118428
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 112,196?
The HCF of 112,196 is 28
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 112/834, 196/284?
Answer: GCF of Numerators as per given numbers 112/834, 196/284 is
GCF of Numerators i.e. for 112,196 is 28
LCM of denominators i.e. for 834,284 is 118428.
Thus, GCF of Fractions is 28/118428.Finally, GCF of Fractions for 112/834, 196/284 is 28/118428.