Use our free GCF of Fractions Calculator tool to compute the GCF of 314/756, 779/204 i.e 1/12852 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/756, 779/204.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 314/756,779/204
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 314/756,779/204, numerators are 314,779
Denominators are 756,204
The GCF of 314,779 is 1 .
LCM of 756,204 is 12852.
The greatest common factor of 314/756,779/204 = [GCF of 314,779]/[LCM of 756,204]= 1/12852
Therefore, the GCF of 314/756,779/204 is 1/12852.
To find the highest common factor of 314,779, we have to find the factors of both numbers and list the highest common factor.
The factors of 314 are 1, 2, 157, 314
The factors of 779 are 1, 19, 41, 779
The HCF of 314,779 is 1.
Lets's calculate GCF of 314,779
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 314
:1,2,157,314
Now, list down the factors of 779
:1,19,41,779
Greatest Common Factor
We found the factors 314,779 . The biggest common factor number is the GCF number.
So the greatest common factor 314,779 is 1.
Lets's calculate LCM of 756,204
2 | 756, 204 |
2 | 378, 102 |
3 | 189, 51 |
63, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 63 x 17 = 12852
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12852
Therefore, the GCF of Fractions 314/756,779/204 is 1/12852
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 756,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(756,204) = 12
common factors(in case of two or more numbers have common factors) = 1
GCF(756,204) x common factors =12 x 1 = 12
LCM(756,204) = ( 756 × 204 ) / 12
LCM(756,204) = 154224 / 12
LCM(756,204) = 12852
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 314,779?
The HCF of 314,779 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 314/756, 779/204?
Answer: GCF of Numerators as per given numbers 314/756, 779/204 is
GCF of Numerators i.e. for 314,779 is 1
LCM of denominators i.e. for 756,204 is 12852.
Thus, GCF of Fractions is 1/12852.Finally, GCF of Fractions for 314/756, 779/204 is 1/12852.