Use our free GCF of Fractions Calculator tool to compute the GCF of 834/337, 864/774 i.e 6/260838 easily. The following is the detailed procedure to determine the greatest common factor of fractions 834/337, 864/774.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 834/337,864/774
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 834/337,864/774, numerators are 834,864
Denominators are 337,774
The GCF of 834,864 is 6 .
LCM of 337,774 is 260838.
The greatest common factor of 834/337,864/774 = [GCF of 834,864]/[LCM of 337,774]= 6/260838
Therefore, the GCF of 834/337,864/774 is 6/260838.
To find the highest common factor of 834,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 834 are 1, 2, 3, 6, 139, 278, 417, 834
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 834,864 is 6.
Lets's calculate GCF of 834,864
2 | 834, 864 |
3 | 417, 432 |
139, 144 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 834
:1,2,3,6,139,278,417,834
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 834,864 . The biggest common factor number is the GCF number.
So the greatest common factor 834,864 is 6.
Lets's calculate LCM of 337,774
Given numbers has no common factors except 1. So, there LCM is their product i.e 260838
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/260838
Therefore, the GCF of Fractions 834/337,864/774 is 6/260838
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 337,774 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(337,774) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(337,774) x common factors =1 x 1 = 1
LCM(337,774) = ( 337 × 774 ) / 1
LCM(337,774) = 260838 / 1
LCM(337,774) = 260838
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 834,864?
The HCF of 834,864 is 6
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 834/337, 864/774?
Answer: GCF of Numerators as per given numbers 834/337, 864/774 is
GCF of Numerators i.e. for 834,864 is 6
LCM of denominators i.e. for 337,774 is 260838.
Thus, GCF of Fractions is 6/260838.Finally, GCF of Fractions for 834/337, 864/774 is 6/260838.