Use our free GCF of Fractions Calculator tool to compute the GCF of 561/945, 218/984 i.e 1/309960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 561/945, 218/984.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 561/945,218/984
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 561/945,218/984, numerators are 561,218
Denominators are 945,984
The GCF of 561,218 is 1 .
LCM of 945,984 is 309960.
The greatest common factor of 561/945,218/984 = [GCF of 561,218]/[LCM of 945,984]= 1/309960
Therefore, the GCF of 561/945,218/984 is 1/309960.
To find the highest common factor of 561,218, we have to find the factors of both numbers and list the highest common factor.
The factors of 561 are 1, 3, 11, 17, 33, 51, 187, 561
The factors of 218 are 1, 2, 109, 218
The HCF of 561,218 is 1.
Lets's calculate GCF of 561,218
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 561
:1,3,11,17,33,51,187,561
Now, list down the factors of 218
:1,2,109,218
Greatest Common Factor
We found the factors 561,218 . The biggest common factor number is the GCF number.
So the greatest common factor 561,218 is 1.
Lets's calculate LCM of 945,984
3 | 945, 984 |
315, 328 |
∴ So the LCM of the given numbers is 3 x 315 x 328 = 309960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/309960
Therefore, the GCF of Fractions 561/945,218/984 is 1/309960
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 945,984 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(945,984) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(945,984) x common factors =3 x 1 = 3
LCM(945,984) = ( 945 × 984 ) / 3
LCM(945,984) = 929880 / 3
LCM(945,984) = 309960
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 561,218?
The HCF of 561,218 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 561/945, 218/984?
Answer: GCF of Numerators as per given numbers 561/945, 218/984 is
GCF of Numerators i.e. for 561,218 is 1
LCM of denominators i.e. for 945,984 is 309960.
Thus, GCF of Fractions is 1/309960.Finally, GCF of Fractions for 561/945, 218/984 is 1/309960.