Use our free GCF of Fractions Calculator tool to compute the GCF of 107/343, 974/309 i.e 1/105987 easily. The following is the detailed procedure to determine the greatest common factor of fractions 107/343, 974/309.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 107/343,974/309
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 107/343,974/309, numerators are 107,974
Denominators are 343,309
The GCF of 107,974 is 1 .
LCM of 343,309 is 105987.
The greatest common factor of 107/343,974/309 = [GCF of 107,974]/[LCM of 343,309]= 1/105987
Therefore, the GCF of 107/343,974/309 is 1/105987.
To find the highest common factor of 107,974, we have to find the factors of both numbers and list the highest common factor.
The factors of 107 are 1, 107
The factors of 974 are 1, 2, 487, 974
The HCF of 107,974 is 1.
Lets's calculate GCF of 107,974
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 107
:1,107
Now, list down the factors of 974
:1,2,487,974
Greatest Common Factor
We found the factors 107,974 . The biggest common factor number is the GCF number.
So the greatest common factor 107,974 is 1.
Lets's calculate LCM of 343,309
Given numbers has no common factors except 1. So, there LCM is their product i.e 105987
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/105987
Therefore, the GCF of Fractions 107/343,974/309 is 1/105987
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 343,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,309) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(343,309) x common factors =1 x 1 = 1
LCM(343,309) = ( 343 × 309 ) / 1
LCM(343,309) = 105987 / 1
LCM(343,309) = 105987
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 107,974?
The HCF of 107,974 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 107/343, 974/309?
Answer: GCF of Numerators as per given numbers 107/343, 974/309 is
GCF of Numerators i.e. for 107,974 is 1
LCM of denominators i.e. for 343,309 is 105987.
Thus, GCF of Fractions is 1/105987.Finally, GCF of Fractions for 107/343, 974/309 is 1/105987.