Use our free GCF of Fractions Calculator tool to compute the GCF of 812/909, 434/366 i.e 14/110898 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/909, 434/366.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 812/909,434/366
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 812/909,434/366, numerators are 812,434
Denominators are 909,366
The GCF of 812,434 is 14 .
LCM of 909,366 is 110898.
The greatest common factor of 812/909,434/366 = [GCF of 812,434]/[LCM of 909,366]= 14/110898
Therefore, the GCF of 812/909,434/366 is 14/110898.
To find the highest common factor of 812,434, 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 434 are 1, 2, 7, 14, 31, 62, 217, 434
The HCF of 812,434 is 14.
Lets's calculate GCF of 812,434
2 | 812, 434 |
7 | 406, 217 |
58, 31 |
∴ So the GCF of the given numbers is 2 x 7 = 14
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 434
:1,2,7,14,31,62,217,434
Greatest Common Factor
We found the factors 812,434 . The biggest common factor number is the GCF number.
So the greatest common factor 812,434 is 14.
Lets's calculate LCM of 909,366
3 | 909, 366 |
303, 122 |
∴ So the LCM of the given numbers is 3 x 303 x 122 = 110898
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/110898
Therefore, the GCF of Fractions 812/909,434/366 is 14/110898
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 909,366 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(909,366) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(909,366) x common factors =3 x 1 = 3
LCM(909,366) = ( 909 × 366 ) / 3
LCM(909,366) = 332694 / 3
LCM(909,366) = 110898
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 812,434?
The HCF of 812,434 is 14
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 812/909, 434/366?
Answer: GCF of Numerators as per given numbers 812/909, 434/366 is
GCF of Numerators i.e. for 812,434 is 14
LCM of denominators i.e. for 909,366 is 110898.
Thus, GCF of Fractions is 14/110898.Finally, GCF of Fractions for 812/909, 434/366 is 14/110898.