Use our free GCF of Fractions Calculator tool to compute the GCF of 66/73, 34/394, 164/706 i.e 2/10152986 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/73, 34/394, 164/706.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/73,34/394,164/706
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 66/73,34/394,164/706, numerators are 66,34,164
Denominators are 73,394,706
The GCF of 66,34,164 is 2 .
LCM of 73,394,706 is 10152986.
The greatest common factor of 66/73,34/394,164/706 = [GCF of 66,34,164]/[LCM of 73,394,706]= 2/10152986
Therefore, the GCF of 66/73,34/394,164/706 is 2/10152986.
To find the highest common factor of 66,34,164, we have to find the factors of both numbers and list the highest common factor.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, 66
The factors of 34 are 1, 2, 17, 34
The factors of 164 are 1, 2, 4, 41, 82, 164
The HCF of 66,34,164 is 2.
Lets's calculate GCF of 66,34,164
2 | 66, 34, 164 |
33, 17, 82 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 34
:1,2,17,34
Now, list down the factors of 164
:1,2,4,41,82,164
Greatest Common Factor
We found the factors 66,34,164 . The biggest common factor number is the GCF number.
So the greatest common factor 66,34,164 is 2.
Lets's calculate LCM of 73,394,706
2 | 73, 394, 706 |
73, 197, 353 |
∴ So the LCM of the given numbers is 2 x 73 x 197 x 353 = 10152986
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10152986
Therefore, the GCF of Fractions 66/73,34/394,164/706 is 2/10152986
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 73,394,706 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(73,394,706) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(73,394,706) x common factors =1 x 2 = 2
LCM(73,394,706) = ( 73 × 394 × 706 ) / 2
LCM(73,394,706) = 20305972 / 2
LCM(73,394,706) = 10152986
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 66,34,164?
The HCF of 66,34,164 is 2
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 66/73, 34/394, 164/706?
Answer: GCF of Numerators as per given numbers 66/73, 34/394, 164/706 is
GCF of Numerators i.e. for 66,34,164 is 2
LCM of denominators i.e. for 73,394,706 is 10152986.
Thus, GCF of Fractions is 2/10152986.Finally, GCF of Fractions for 66/73, 34/394, 164/706 is 2/10152986.