Use our free GCF of Fractions Calculator tool to compute the GCF of 812/382, 680/766 i.e 4/146306 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/382, 680/766.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 812/382,680/766
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 812/382,680/766, numerators are 812,680
Denominators are 382,766
The GCF of 812,680 is 4 .
LCM of 382,766 is 146306.
The greatest common factor of 812/382,680/766 = [GCF of 812,680]/[LCM of 382,766]= 4/146306
Therefore, the GCF of 812/382,680/766 is 4/146306.
To find the highest common factor of 812,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 812,680 is 4.
Lets's calculate GCF of 812,680
2 | 812, 680 |
2 | 406, 340 |
203, 170 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 812,680 . The biggest common factor number is the GCF number.
So the greatest common factor 812,680 is 4.
Lets's calculate LCM of 382,766
2 | 382, 766 |
191, 383 |
∴ So the LCM of the given numbers is 2 x 191 x 383 = 146306
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/146306
Therefore, the GCF of Fractions 812/382,680/766 is 4/146306
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 382,766 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,766) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(382,766) x common factors =2 x 1 = 2
LCM(382,766) = ( 382 × 766 ) / 2
LCM(382,766) = 292612 / 2
LCM(382,766) = 146306
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 812,680?
The HCF of 812,680 is 4
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 812/382, 680/766?
Answer: GCF of Numerators as per given numbers 812/382, 680/766 is
GCF of Numerators i.e. for 812,680 is 4
LCM of denominators i.e. for 382,766 is 146306.
Thus, GCF of Fractions is 4/146306.Finally, GCF of Fractions for 812/382, 680/766 is 4/146306.