Use our free GCF of Fractions Calculator tool to compute the GCF of 726/194, 994/109 i.e 2/21146 easily. The following is the detailed procedure to determine the greatest common factor of fractions 726/194, 994/109.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 726/194,994/109
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 726/194,994/109, numerators are 726,994
Denominators are 194,109
The GCF of 726,994 is 2 .
LCM of 194,109 is 21146.
The greatest common factor of 726/194,994/109 = [GCF of 726,994]/[LCM of 194,109]= 2/21146
Therefore, the GCF of 726/194,994/109 is 2/21146.
To find the highest common factor of 726,994, we have to find the factors of both numbers and list the highest common factor.
The factors of 726 are 1, 2, 3, 6, 11, 22, 33, 66, 121, 242, 363, 726
The factors of 994 are 1, 2, 7, 14, 71, 142, 497, 994
The HCF of 726,994 is 2.
Lets's calculate GCF of 726,994
2 | 726, 994 |
363, 497 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 726
:1,2,3,6,11,22,33,66,121,242,363,726
Now, list down the factors of 994
:1,2,7,14,71,142,497,994
Greatest Common Factor
We found the factors 726,994 . The biggest common factor number is the GCF number.
So the greatest common factor 726,994 is 2.
Lets's calculate LCM of 194,109
Given numbers has no common factors except 1. So, there LCM is their product i.e 21146
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21146
Therefore, the GCF of Fractions 726/194,994/109 is 2/21146
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 194,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(194,109) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(194,109) x common factors =1 x 1 = 1
LCM(194,109) = ( 194 × 109 ) / 1
LCM(194,109) = 21146 / 1
LCM(194,109) = 21146
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 726,994?
The HCF of 726,994 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 726/194, 994/109?
Answer: GCF of Numerators as per given numbers 726/194, 994/109 is
GCF of Numerators i.e. for 726,994 is 2
LCM of denominators i.e. for 194,109 is 21146.
Thus, GCF of Fractions is 2/21146.Finally, GCF of Fractions for 726/194, 994/109 is 2/21146.