Use our free GCF of Fractions Calculator tool to compute the GCF of 696/117, 284/138 i.e 4/5382 easily. The following is the detailed procedure to determine the greatest common factor of fractions 696/117, 284/138.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 696/117,284/138
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 696/117,284/138, numerators are 696,284
Denominators are 117,138
The GCF of 696,284 is 4 .
LCM of 117,138 is 5382.
The greatest common factor of 696/117,284/138 = [GCF of 696,284]/[LCM of 117,138]= 4/5382
Therefore, the GCF of 696/117,284/138 is 4/5382.
To find the highest common factor of 696,284, we have to find the factors of both numbers and list the highest common factor.
The factors of 696 are 1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696
The factors of 284 are 1, 2, 4, 71, 142, 284
The HCF of 696,284 is 4.
Lets's calculate GCF of 696,284
2 | 696, 284 |
2 | 348, 142 |
174, 71 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 696
:1,2,3,4,6,8,12,24,29,58,87,116,174,232,348,696
Now, list down the factors of 284
:1,2,4,71,142,284
Greatest Common Factor
We found the factors 696,284 . The biggest common factor number is the GCF number.
So the greatest common factor 696,284 is 4.
Lets's calculate LCM of 117,138
3 | 117, 138 |
39, 46 |
∴ So the LCM of the given numbers is 3 x 39 x 46 = 5382
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/5382
Therefore, the GCF of Fractions 696/117,284/138 is 4/5382
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 117,138 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(117,138) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(117,138) x common factors =3 x 1 = 3
LCM(117,138) = ( 117 × 138 ) / 3
LCM(117,138) = 16146 / 3
LCM(117,138) = 5382
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 696,284?
The HCF of 696,284 is 4
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 696/117, 284/138?
Answer: GCF of Numerators as per given numbers 696/117, 284/138 is
GCF of Numerators i.e. for 696,284 is 4
LCM of denominators i.e. for 117,138 is 5382.
Thus, GCF of Fractions is 4/5382.Finally, GCF of Fractions for 696/117, 284/138 is 4/5382.