Use our free GCF of Fractions Calculator tool to compute the GCF of 66/218, 997/321, 198/678 i.e 1/7907514 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/218, 997/321, 198/678.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/218,997/321,198/678
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 66/218,997/321,198/678, numerators are 66,997,198
Denominators are 218,321,678
The GCF of 66,997,198 is 1 .
LCM of 218,321,678 is 7907514.
The greatest common factor of 66/218,997/321,198/678 = [GCF of 66,997,198]/[LCM of 218,321,678]= 1/7907514
Therefore, the GCF of 66/218,997/321,198/678 is 1/7907514.
To find the highest common factor of 66,997,198, 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 997 are 1, 997
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 66,997,198 is 1.
Lets's calculate GCF of 66,997,198
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 997
:1,997
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 66,997,198 . The biggest common factor number is the GCF number.
So the greatest common factor 66,997,198 is 1.
Lets's calculate LCM of 218,321,678
2 | 218, 321, 678 |
3 | 109, 321, 339 |
109, 107, 113 |
∴ So the LCM of the given numbers is 2 x 3 x 109 x 107 x 113 = 7907514
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7907514
Therefore, the GCF of Fractions 66/218,997/321,198/678 is 1/7907514
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 218,321,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(218,321,678) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(218,321,678) x common factors =1 x 6 = 6
LCM(218,321,678) = ( 218 × 321 × 678 ) / 6
LCM(218,321,678) = 47445084 / 6
LCM(218,321,678) = 7907514
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 66,997,198?
The HCF of 66,997,198 is 1
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 66/218, 997/321, 198/678?
Answer: GCF of Numerators as per given numbers 66/218, 997/321, 198/678 is
GCF of Numerators i.e. for 66,997,198 is 1
LCM of denominators i.e. for 218,321,678 is 7907514.
Thus, GCF of Fractions is 1/7907514.Finally, GCF of Fractions for 66/218, 997/321, 198/678 is 1/7907514.