Use our free GCF of Fractions Calculator tool to compute the GCF of 35/37, 686/39, 868/314 i.e 7/453102 easily. The following is the detailed procedure to determine the greatest common factor of fractions 35/37, 686/39, 868/314.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/37,686/39,868/314
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 35/37,686/39,868/314, numerators are 35,686,868
Denominators are 37,39,314
The GCF of 35,686,868 is 7 .
LCM of 37,39,314 is 453102.
The greatest common factor of 35/37,686/39,868/314 = [GCF of 35,686,868]/[LCM of 37,39,314]= 7/453102
Therefore, the GCF of 35/37,686/39,868/314 is 7/453102.
To find the highest common factor of 35,686,868, we have to find the factors of both numbers and list the highest common factor.
The factors of 35 are 1, 5, 7, 35
The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686
The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868
The HCF of 35,686,868 is 7.
Lets's calculate GCF of 35,686,868
7 | 35, 686, 868 |
5, 98, 124 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 35
:1,5,7,35
Now, list down the factors of 686
:1,2,7,14,49,98,343,686
Now, list down the factors of 868
:1,2,4,7,14,28,31,62,124,217,434,868
Greatest Common Factor
We found the factors 35,686,868 . The biggest common factor number is the GCF number.
So the greatest common factor 35,686,868 is 7.
Lets's calculate LCM of 37,39,314
Given numbers has no common factors except 1. So, there LCM is their product i.e 453102
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/453102
Therefore, the GCF of Fractions 35/37,686/39,868/314 is 7/453102
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 37,39,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(37,39,314) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(37,39,314) x common factors =1 x 1 = 1
LCM(37,39,314) = ( 37 × 39 × 314 ) / 1
LCM(37,39,314) = 453102 / 1
LCM(37,39,314) = 453102
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 35,686,868?
The HCF of 35,686,868 is 7
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 35/37, 686/39, 868/314?
Answer: GCF of Numerators as per given numbers 35/37, 686/39, 868/314 is
GCF of Numerators i.e. for 35,686,868 is 7
LCM of denominators i.e. for 37,39,314 is 453102.
Thus, GCF of Fractions is 7/453102.Finally, GCF of Fractions for 35/37, 686/39, 868/314 is 7/453102.