Use our free GCF of Fractions Calculator tool to compute the GCF of 66/57, 222/45, 969/861 i.e 3/245385 easily. The following is the detailed procedure to determine the greatest common factor of fractions 66/57, 222/45, 969/861.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 66/57,222/45,969/861
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 66/57,222/45,969/861, numerators are 66,222,969
Denominators are 57,45,861
The GCF of 66,222,969 is 3 .
LCM of 57,45,861 is 245385.
The greatest common factor of 66/57,222/45,969/861 = [GCF of 66,222,969]/[LCM of 57,45,861]= 3/245385
Therefore, the GCF of 66/57,222/45,969/861 is 3/245385.
To find the highest common factor of 66,222,969, 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 222 are 1, 2, 3, 6, 37, 74, 111, 222
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The HCF of 66,222,969 is 3.
Lets's calculate GCF of 66,222,969
3 | 66, 222, 969 |
22, 74, 323 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 66
:1,2,3,6,11,22,33,66
Now, list down the factors of 222
:1,2,3,6,37,74,111,222
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Greatest Common Factor
We found the factors 66,222,969 . The biggest common factor number is the GCF number.
So the greatest common factor 66,222,969 is 3.
Lets's calculate LCM of 57,45,861
3 | 57, 45, 861 |
19, 15, 287 |
∴ So the LCM of the given numbers is 3 x 19 x 15 x 287 = 245385
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/245385
Therefore, the GCF of Fractions 66/57,222/45,969/861 is 3/245385
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 57,45,861 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(57,45,861) = 3
common factors(in case of two or more numbers have common factors) = 3
GCF(57,45,861) x common factors =3 x 3 = 9
LCM(57,45,861) = ( 57 × 45 × 861 ) / 9
LCM(57,45,861) = 2208465 / 9
LCM(57,45,861) = 245385
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 66,222,969?
The HCF of 66,222,969 is 3
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 66/57, 222/45, 969/861?
Answer: GCF of Numerators as per given numbers 66/57, 222/45, 969/861 is
GCF of Numerators i.e. for 66,222,969 is 3
LCM of denominators i.e. for 57,45,861 is 245385.
Thus, GCF of Fractions is 3/245385.Finally, GCF of Fractions for 66/57, 222/45, 969/861 is 3/245385.