Use our free GCF of Fractions Calculator tool to compute the GCF of 119/123, 194/756 i.e 1/30996 easily. The following is the detailed procedure to determine the greatest common factor of fractions 119/123, 194/756.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 119/123,194/756
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 119/123,194/756, numerators are 119,194
Denominators are 123,756
The GCF of 119,194 is 1 .
LCM of 123,756 is 30996.
The greatest common factor of 119/123,194/756 = [GCF of 119,194]/[LCM of 123,756]= 1/30996
Therefore, the GCF of 119/123,194/756 is 1/30996.
To find the highest common factor of 119,194, we have to find the factors of both numbers and list the highest common factor.
The factors of 119 are 1, 7, 17, 119
The factors of 194 are 1, 2, 97, 194
The HCF of 119,194 is 1.
Lets's calculate GCF of 119,194
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 119
:1,7,17,119
Now, list down the factors of 194
:1,2,97,194
Greatest Common Factor
We found the factors 119,194 . The biggest common factor number is the GCF number.
So the greatest common factor 119,194 is 1.
Lets's calculate LCM of 123,756
3 | 123, 756 |
41, 252 |
∴ So the LCM of the given numbers is 3 x 41 x 252 = 30996
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30996
Therefore, the GCF of Fractions 119/123,194/756 is 1/30996
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 123,756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,756) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(123,756) x common factors =3 x 1 = 3
LCM(123,756) = ( 123 × 756 ) / 3
LCM(123,756) = 92988 / 3
LCM(123,756) = 30996
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 119,194?
The HCF of 119,194 is 1
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 119/123, 194/756?
Answer: GCF of Numerators as per given numbers 119/123, 194/756 is
GCF of Numerators i.e. for 119,194 is 1
LCM of denominators i.e. for 123,756 is 30996.
Thus, GCF of Fractions is 1/30996.Finally, GCF of Fractions for 119/123, 194/756 is 1/30996.