Use our free GCF of Fractions Calculator tool to compute the GCF of 680/446, 168/866 i.e 8/193118 easily. The following is the detailed procedure to determine the greatest common factor of fractions 680/446, 168/866.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 680/446,168/866
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 680/446,168/866, numerators are 680,168
Denominators are 446,866
The GCF of 680,168 is 8 .
LCM of 446,866 is 193118.
The greatest common factor of 680/446,168/866 = [GCF of 680,168]/[LCM of 446,866]= 8/193118
Therefore, the GCF of 680/446,168/866 is 8/193118.
To find the highest common factor of 680,168, we have to find the factors of both numbers and list the highest common factor.
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The HCF of 680,168 is 8.
Lets's calculate GCF of 680,168
2 | 680, 168 |
2 | 340, 84 |
2 | 170, 42 |
85, 21 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Greatest Common Factor
We found the factors 680,168 . The biggest common factor number is the GCF number.
So the greatest common factor 680,168 is 8.
Lets's calculate LCM of 446,866
2 | 446, 866 |
223, 433 |
∴ So the LCM of the given numbers is 2 x 223 x 433 = 193118
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/193118
Therefore, the GCF of Fractions 680/446,168/866 is 8/193118
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 446,866 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(446,866) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(446,866) x common factors =2 x 1 = 2
LCM(446,866) = ( 446 × 866 ) / 2
LCM(446,866) = 386236 / 2
LCM(446,866) = 193118
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 680,168?
The HCF of 680,168 is 8
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 680/446, 168/866?
Answer: GCF of Numerators as per given numbers 680/446, 168/866 is
GCF of Numerators i.e. for 680,168 is 8
LCM of denominators i.e. for 446,866 is 193118.
Thus, GCF of Fractions is 8/193118.Finally, GCF of Fractions for 680/446, 168/866 is 8/193118.