Use our free GCF of Fractions Calculator tool to compute the GCF of 138/354, 684/993 i.e 6/117174 easily. The following is the detailed procedure to determine the greatest common factor of fractions 138/354, 684/993.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 138/354,684/993
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 138/354,684/993, numerators are 138,684
Denominators are 354,993
The GCF of 138,684 is 6 .
LCM of 354,993 is 117174.
The greatest common factor of 138/354,684/993 = [GCF of 138,684]/[LCM of 354,993]= 6/117174
Therefore, the GCF of 138/354,684/993 is 6/117174.
To find the highest common factor of 138,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 138 are 1, 2, 3, 6, 23, 46, 69, 138
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 138,684 is 6.
Lets's calculate GCF of 138,684
2 | 138, 684 |
3 | 69, 342 |
23, 114 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 138
:1,2,3,6,23,46,69,138
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 138,684 . The biggest common factor number is the GCF number.
So the greatest common factor 138,684 is 6.
Lets's calculate LCM of 354,993
3 | 354, 993 |
118, 331 |
∴ So the LCM of the given numbers is 3 x 118 x 331 = 117174
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/117174
Therefore, the GCF of Fractions 138/354,684/993 is 6/117174
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 354,993 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,993) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(354,993) x common factors =3 x 1 = 3
LCM(354,993) = ( 354 × 993 ) / 3
LCM(354,993) = 351522 / 3
LCM(354,993) = 117174
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 138,684?
The HCF of 138,684 is 6
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 138/354, 684/993?
Answer: GCF of Numerators as per given numbers 138/354, 684/993 is
GCF of Numerators i.e. for 138,684 is 6
LCM of denominators i.e. for 354,993 is 117174.
Thus, GCF of Fractions is 6/117174.Finally, GCF of Fractions for 138/354, 684/993 is 6/117174.